Abelian Chern-Simons theory and contact torsion
DEFF Research Database (Denmark)
McLellan, Brendan Donald Kenneth
2013-01-01
Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected and abelian. A shift reduced abelian Chern-Simons partition function is introduced using an alternative formulation of the partition function using formal ideas in ...... in quantum field theory. We compare the shift reduced partition function with other formulations of the abelian Chern-Simons partition function. This study naturally motivates an Atiyah-Patodi-Singer type index problem in contact geometry.......Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected and abelian. A shift reduced abelian Chern-Simons partition function is introduced using an alternative formulation of the partition function using formal ideas...
Dimensional regularisation of Chern-Simons field theory
International Nuclear Information System (INIS)
Martin, C.P.
1990-01-01
We discuss the dimensional regularisation program as applied to a pure Chern-Simons theory in Minkowski space. In order to make this regularisation program feasible, we propose adding a Yang-Mills term to the pure Chern-Simons action. It is argued that the pure Chern-Simons theory is recovered in a certain limit. Explicit computations are carried out at the one-loop level in the background field gauge. (orig.)
Localization in abelian Chern-Simons theory
DEFF Research Database (Denmark)
McLellan, Brendan Donald Kenneth
2013-01-01
Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected, and abelian. The abelian Chern-Simons partition function is derived using the Faddeev-Popov gauge fixing method. The partition function is then formally computed...
Chern-Simons theory from first principles
International Nuclear Information System (INIS)
Marino, E.C.
1994-01-01
A review is made of the main properties of the Chern-Simons field theory. These include the dynamical mass generation to the photon without a Higgs field, the statistical transmutation of charged particles coupled to it and the natural appearance of a transverse conductivity. A review of standard theories proposed for the Quantum Hall Effect which use the Chern-Simons term is also made, emphasizing the fact that this terms is put in an artificial manner. A physical origin for the Chern-Simons term is proposed, starting from QED in 3+1 D with the topological term and imposing that the motion of charged matter is restricted to an infinite plane. (author). 12 refs
Teichmüller TQFT vs. Chern-Simons theory
Mikhaylov, Victor
2018-04-01
Teichmüller TQFT is a unitary 3d topological theory whose Hilbert spaces are spanned by Liouville conformal blocks. It is related but not identical to PSL(2, ℝ) Chern-Simons theory. To physicists, it is known in particular in the context of 3d-3d correspondence and also in the holographic description of Virasoro conformal blocks. We propose that this theory can be defined by an analytically-continued Chern-Simons path-integral with an unusual integration cycle. On hyperbolic three-manifolds, this cycle is singled out by the requirement of invertible vielbein. Mathematically, our proposal translates a known conjecture by Andersen and Kashaev into a conjecture about the Kapustin-Witten equations. We further explain that Teichmüller TQFT is dual to complex SL(2, ℂ) Chern-Simons theory at integer level k = 1, clarifying some puzzles previously encountered in the 3d-3d correspondence literature. We also present a new simple derivation of complex Chern-Simons theories from the 6d (2,0) theory on a lens space with a transversely-holomorphic foliation.
Lecture notes on Chern-Simons-Witten theory
Hu, Sen
2001-01-01
This invaluable monograph has arisen in part from E Witten's lectures on topological quantum field theory in the spring of 1989 at Princeton University. At that time Witten unified several important mathematical works in terms of quantum field theory, most notably the Donaldson polynomial, the Gromov-Floer homology and the Jones polynomials. In his lectures, among other things, Witten explained his intrinsic three-dimensional construction of Jones polynomials via Chern-Simons gauge theory. He provided both a rigorous proof of the geometric quantization of the Chern-Simons action and a very ill
4D edge currents from 5D Chern-Simons theory
International Nuclear Information System (INIS)
Gupta, K.S.; Stern, A.
1995-01-01
A class of two dimensional conformal field theories is known to correspond to three dimensional Chern-Simons theory. Here we claim that there is an analogous class of four dimensional field theories corresponding to five dimensional Chern-Simons theory. The four dimensional theories give a coupling between a scalar field and an external divergenceless vector field and they may have some application in magnetohydrodynamics. Like in conformal theories they possess a diffeomorphism symmetry, which for us is along the direction of the vector field, and their generators are analogous to Virasoro generators. Our analysis of the abelian Chern-Simons system uses elementary canonical methods for the quantization of field theories defined on manifolds with boundaries. Edge states appear for these systems and they yield a four dimensional current algebra. We examine the quantization of these algebras in several special cases and claim that a renormalization of the 5D Chern-Simons coupling is necessary for removing divergences. ((orig.))
Abelian Chern-Simons theory and linking numbers via oscillatory integrals
International Nuclear Information System (INIS)
Albeverio, S.; Schaefer, J.
1994-06-01
We introduce a rigorous mathematical model of abelian Chern-Simons theory based on the theory of infinite dimensional oscillatory integrals developed by Albeverio and Hoeegh-Krohn. We construct a gauge-fixed Chern-Simons path integral as a Fresnel integral in a certain Hilbert space. Wilson loop variables are defined as Fresnel integrable functions and it is shown in this context that the expectation value of products of Wilson loops w.r.t. the Chern-Simons path integral is a topological invariant which can be computed in terms of pairwise linking numbers of the loops, as conjectured by Witten. We also propose a lattice Chern-Simons action which converges to the continuum limit. (orig.)
On the non-renormalization properties of Gauge theories with Chern-Simons term
International Nuclear Information System (INIS)
Del Cima, Oswaldo M.; Piguet, Olivier
1997-12-01
Considering three-dimensional Chern-Simons theory, either coupled to matter or with a Yang-Mills term, we show the validity of a trace identity, playing the role of a local form of the Callan-Symanzik equation, in all orders of perturbation theory. From this we deduce the vanishing of the β-function associated to the Chern-Simons coupling constant and the full finiteness in the case of the Yang-Mills Chern-Simons theory. The main ingredient in the proof of the latter property is the non invariance of the Chern-Simons from under the gauge transformations. Our results hold for the three-dimensional Chern-Simons model in a general Riemannian manifold. (author)
The A-polynomial in Chern-Simons theory
DEFF Research Database (Denmark)
Malusà, Alessandro
One of the most amusing aspects of mathematical physics is the great variety of areas of mathematics it relates to, and builds bridges between. The world of TQFT’s, and in particular Chern-Simons, relates to algebraic geometry via the theory of moduli spaces: one example of this is given by the A......-polynomial. This knot invariant is obtained from the algebraic geometry of character varieties, and takes the meaning of the equation of a constraint central in Chern-Simons theory. In my poster I wish to expose the construction of this invariant, and highlight its strong ties with mathematical physics....
A stringy origin of M2 brane Chern-Simons theories
International Nuclear Information System (INIS)
Aganagic, Mina
2010-01-01
We show that string duality relates M-theory on a local Calabi-Yau fourfold singularity X 4 to type IIA string theory on a Calabi-Yau threefold X 3 fibered over a real line, with RR 2-form fluxes turned on. The RR flux encodes how the M-theory circle is fibered over the IIA geometry. The theories on N D2 branes probing X 3 are the well-known quiver theories with N=2 supersymmetry in three dimensions. We show that turning on fluxes, and fibering the X 3 over a direction transverse to the branes, corresponds to turning on N=2 Chern-Simons couplings. String duality implies that, in the strong coupling limit, the N D2 branes on X 3 in this background become N M2 branes on X 4 . This provides a string theory derivation for the recently conjectured description of the M2 brane theories on Calabi-Yau fourfolds in terms of N=2 quiver Chern-Simons theories. We also provide a new N=2 Chern-Simons theory dual to AdS 4 xQ 1,1,1 . Type IIA/M-theory duality also relates IIA string theory on X 3 with only the RR fluxes turned on, to M-theory on a G 2 holonomy manifold. We show that this implies that the N M2 branes probing the G 2 manifold are described by the quiver Chern-Simons theory originating from the D2 branes probing X 3 , except that now Chern-Simons terms preserve only N=1 supersymmetry in three dimensions.
Combinatorial quantization of the Hamiltonian Chern-Simons theory
International Nuclear Information System (INIS)
Alekseev, A.Yu.; Grosse, H.; Schomerus, V.
1996-01-01
This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathematically rigorous definition of the algebra of observables A CS of the Chern Simons model. It is a *-algebra of ''functions on the quantum moduli space of flat connections'' and comes equipped with a positive functional ω (''integration''). We prove that this data does not depend on the particular choices which have been made in the construction. The algebra A CS provides a deformation quantization of the algebra of functions on the moduli space along the natural Poisson bracket induced by the Chern Simons action. We evaluate a volume of the quantized moduli space and prove that it coincides with the Verlinde number. This answer is also interpreted as a partition partition function of the lattice Yang-Mills theory corresponding to a quantum gauge group. (orig.). With 1 fig
Anyons in discrete gauge theories with Chern-Simons terms
International Nuclear Information System (INIS)
Bais, F.A.; Driel, P. van; Wild Propitius, M. de
1993-01-01
A gauge theory with a discrete group H in (2+1)-dimensional space-time is known to describe (non-abelian) anyons. We study the effect of adding a Chern-Simons term to such a theory. As in a previous paper, we emphasize the algebraic structure underlying a discrete H gauge theory, namely the Hopf algebra D(H). For H≅Z N , we argue on physical grounds that a Chern-Simons term in the action leads to a non-trivial 3-cocycle on D(H). Accordingly, the physically inequivalent models are labeled by the elements of the cohomology group H 3 (H, U(1)). It depends periodically on the coefficient of the Chern-Simons term which model is realized. This establishes a relation with the discrete topological field theories of Dijkgraaf and Witten. We extrapolate these results to non-abelian H, and work out the representative example H≅anti D 2 . (orig.)
Wavefunction of the Universe and Chern-Simons perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Soo Chopin [Department of Physics, National Cheng Kung University Tainan 70101, Taiwan (China)
2002-03-21
The Chern-Simons exact solution of four-dimensional quantum gravity with nonvanishing cosmological constant is presented in metric variables as the partition function of Chern-Simons theory with nontrivial source. The perturbative expansion is given, and the wavefunction is computed to the lowest order of approximation for the Cauchy surface which is topologically a 3-sphere. The state is well-defined even at degenerate and vanishing values of the dreibein. Reality conditions for the Ashtekar variables are also taken into account, and remarkable features of the Chern-Simons state and their relevance to cosmology are pointed out.
Chern-Simons theory and three-dimensional surfaces
International Nuclear Information System (INIS)
Guven, Jemal
2007-01-01
There are two natural Chern-Simons theories associated with the embedding of a three-dimensional surface in Euclidean space: one is constructed using the induced metric connection and involves only the intrinsic geometry? the other is extrinsic and uses the connection associated with the gauging of normal rotations. As such, the two theories appear to describe very different aspects of the surface geometry. Remarkably, at a classical level, they are equivalent. In particular, it will be shown that their stress tensors differ only by a null contribution. Their Euler-Lagrange equations provide identical constraints on the normal curvature. A new identity for the Cotton tensor is associated with the triviality of the Chern-Simons theory for embedded hypersurfaces implied by this equivalence
Chern-Simons matrix models, two-dimensional Yang-Mills theory and the Sutherland model
International Nuclear Information System (INIS)
Szabo, Richard J; Tierz, Miguel
2010-01-01
We derive some new relationships between matrix models of Chern-Simons gauge theory and of two-dimensional Yang-Mills theory. We show that q-integration of the Stieltjes-Wigert matrix model is the discrete matrix model that describes q-deformed Yang-Mills theory on S 2 . We demonstrate that the semiclassical limit of the Chern-Simons matrix model is equivalent to the Gross-Witten model in the weak-coupling phase. We study the strong-coupling limit of the unitary Chern-Simons matrix model and show that it too induces the Gross-Witten model, but as a first-order deformation of Dyson's circular ensemble. We show that the Sutherland model is intimately related to Chern-Simons gauge theory on S 3 , and hence to q-deformed Yang-Mills theory on S 2 . In particular, the ground-state wavefunction of the Sutherland model in its classical equilibrium configuration describes the Chern-Simons free energy. The correspondence is extended to Wilson line observables and to arbitrary simply laced gauge groups.
Canonical sectors of five-dimensional Chern-Simons theories
International Nuclear Information System (INIS)
Miskovic, Olivera; Troncoso, Ricardo; Zanelli, Jorge
2005-01-01
The dynamics of five-dimensional Chern-Simons theories is analyzed. These theories are characterized by intricate self couplings which give rise to dynamical features not present in standard theories. As a consequence, Dirac's canonical formalism cannot be directly applied due to the presence of degeneracies of the symplectic form and irregularities of the constraints on some surfaces of phase space, obscuring the dynamical content of these theories. Here we identify conditions that define sectors where the canonical formalism can be applied for a class of non-Abelian Chern-Simons theories, including supergravity. A family of solutions satisfying the canonical requirements is explicitly found. The splitting between first and second class constraints is performed around these backgrounds, allowing the construction of the charge algebra, including its central extension
Shift versus no-shift in local regularization of Chern-Simons theory
International Nuclear Information System (INIS)
Giavarini, G.; Parma Univ.; Martin, C.P.; Ruiz Ruiz, F.
1994-01-01
We consider a family of local BRS-invariant higher covariant derivative regularizations of SU(N) Chern-Simons theory that do not shift the value of the Chern-Simons parameter k to k + sign(k) c v at one loop. (orig.)
Transport in Chern-Simons-matter theories
Energy Technology Data Exchange (ETDEWEB)
Gur-Ari, Guy; Hartnoll, Sean; Mahajan, Raghu [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States)
2016-07-18
The frequency-dependent longitudinal and Hall conductivities — σ{sub xx} and σ{sub xy} — are dimensionless functions of ω/T in 2+1 dimensional CFTs at nonzero temperature. These functions characterize the spectrum of charged excitations of the theory and are basic experimental observables. We compute these conductivities for large N Chern-Simons theory with fermion matter. The computation is exact in the ’t Hooft coupling λ at N=∞. We describe various physical features of the conductivity, including an explicit relation between the weight of the delta function at ω=0 in σ{sub xx} and the existence of infinitely many higher spin conserved currents in the theory. We also compute the conductivities perturbatively in Chern-Simons theory with scalar matter and show that the resulting functions of ω/T agree with the strong coupling fermionic result. This provides a new test of the conjectured 3d bosonization duality. In matching the Hall conductivities we resolve an outstanding puzzle by carefully treating an extra anomaly that arises in the regularization scheme used.
Tertiary classes–after Chern-Simons theory
Indian Academy of Sciences (India)
J.N. Iyer Institute of Mathematical Sciences Chennai, India
2013-11-08
Nov 8, 2013 ... Euler characteristic class. In early twentieth century, the notion of local product structure, i.e. fiber spaces and their generalizations appeared, in the study of topological spaces (with additional structures). J.N. Iyer. IMSc, Chennai. Tertiary classes–after Chern-Simons theory ...
Chern-Simons gauge theory on orbifolds: Open strings from three dimensions
Hořava, Petr
1996-12-01
Chern-Simons gauge theory is formulated on three-dimensional Z2 orbifolds. The locus of singular points on a given orbifold is equivalent to a link of Wilson lines. This allows one to reduce any correlation function on orbifolds to a sum of more complicated correlation functions in the simpler theory on manifolds. Chern-Simons theory on manifolds is known to be related to two-dimensional (2D) conformal field theory (CFT) on closed-string surfaces; here it is shown that the theory on orbifolds is related to 2D CFT of unoriented closed- and open-string models, i.e. to worldsheet orbifold models. In particular, the boundary components of the worldsheet correspond to the components of the singular locus in the 3D orbifold. This correspondence leads to a simple identification of the open-string spectra, including their Chan-Paton degeneration, in terms of fusing Wilson lines in the corresponding Chern-Simons theory. The correspondence is studied in detail, and some exactly solvable examples are presented. Some of these examples indicate that it is natural to think of the orbifold group Z2 as a part of the gauge group of the Chern-Simons theory, thus generalizing the standard definition of gauge theories.
Chern-Simons as a geometrical set up for three dimensional gauge theories
International Nuclear Information System (INIS)
Lemes, V.E.R; Jesus, C. Linhares de; Sorella, S.P.; Villar, L.C.Q.; Ventura, O.S.
1997-12-01
Three dimensional Yang-Mills gauge theories in the presence of the Chern-Simons action are seen as being generated by the pure topological Chern-Simons term through nonlinear covariant redefinitions of the gauge field. (author)
Abelian Chern endash Simons theory. I. A topological quantum field theory
International Nuclear Information System (INIS)
Manoliu, M.
1998-01-01
We give a construction of the Abelian Chern endash Simons gauge theory from the point of view of a 2+1-dimensional topological quantum field theory. The definition of the quantum theory relies on geometric quantization ideas that have been previously explored in connection to the non-Abelian Chern endash Simons theory [J. Diff. Geom. 33, 787 endash 902 (1991); Topology 32, 509 endash 529 (1993)]. We formulate the topological quantum field theory in terms of the category of extended 2- and 3-manifolds introduced in a preprint by Walker in 1991 and prove that it satisfies the axioms of unitary topological quantum field theories formulated by Atiyah [Publ. Math. Inst. Hautes Etudes Sci. Pans 68, 175 endash 186 (1989)]. copyright 1998 American Institute of Physics
Integrable lambda models and Chern-Simons theories
International Nuclear Information System (INIS)
Schmidtt, David M.
2017-01-01
In this note we reveal a connection between the phase space of lambda models on S 1 ×ℝ and the phase space of double Chern-Simons theories on D×ℝ and explain in the process the origin of the non-ultralocality of the Maillet bracket, which emerges as a boundary algebra. In particular, this means that the (classical) AdS 5 ×S 5 lambda model can be understood as a double Chern-Simons theory defined on the Lie superalgebra psu(2,2|4) after a proper dependence of the spectral parameter is introduced. This offers a possibility for avoiding the use of the problematic non-ultralocal Poisson algebras that preclude the introduction of lattice regularizations and the application of the QISM to string sigma models. The utility of the equivalence at the quantum level is, however, still to be explored.
A direct derivation of polynomial invariants from perturbative Chern-Simons gauge theory
International Nuclear Information System (INIS)
Ochiai, Tomoshiro
2003-01-01
There have been several methods to show that the expectation values of Wilson loop operators in the SU(N) Chern-Simons gauge theory satisfy the HOMFLY skein relation. We shall give another method from the perturbative method of the SU(N) Chern-Simons gauge theory in the light-cone gauge, which is more direct than already known methods
Matrix model as a mirror of Chern-Simons theory
International Nuclear Information System (INIS)
Aganagic, Mina; Klemm, Albrecht; Marino, Marcos; Vafa, Cumrun
2004-01-01
Using mirror symmetry, we show that Chern-Simons theory on certain manifolds such as lens spaces reduces to a novel class of Hermitian matrix models, where the measure is that of unitary matrix models. We show that this agrees with the more conventional canonical quantization of Chern-Simons theory. Moreover, large N dualities in this context lead to computation of all genus A-model topological amplitudes on toric Calabi-Yau manifolds in terms of matrix integrals. In the context of type IIA superstring compactifications on these Calabi-Yau manifolds with wrapped D6 branes (which are dual to M-theory on G2 manifolds) this leads to engineering and solving F-terms for N=1 supersymmetric gauge theories with superpotentials involving certain multi-trace operators. (author)
Integrable lambda models and Chern-Simons theories
Energy Technology Data Exchange (ETDEWEB)
Schmidtt, David M. [Departamento de Física, Universidade Federal de São Carlos,Caixa Postal 676, CEP 13565-905, São Carlos-SP (Brazil)
2017-05-03
In this note we reveal a connection between the phase space of lambda models on S{sup 1}×ℝ and the phase space of double Chern-Simons theories on D×ℝ and explain in the process the origin of the non-ultralocality of the Maillet bracket, which emerges as a boundary algebra. In particular, this means that the (classical) AdS{sub 5}×S{sup 5} lambda model can be understood as a double Chern-Simons theory defined on the Lie superalgebra psu(2,2|4) after a proper dependence of the spectral parameter is introduced. This offers a possibility for avoiding the use of the problematic non-ultralocal Poisson algebras that preclude the introduction of lattice regularizations and the application of the QISM to string sigma models. The utility of the equivalence at the quantum level is, however, still to be explored.
Chern-Simons-Rozansky-Witten topological field theory
Energy Technology Data Exchange (ETDEWEB)
Kapustin, Anton [California Institute of Technology, Minor Outlying Islands (United States); Saulina, Natalia [California Institute of Technology, Minor Outlying Islands (United States)], E-mail: saulina@theory.caltech.edu
2009-12-21
We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern-Simons and Rozansky-Witten theory and can be regarded as a topologically-twisted version of the N=4d=3 supersymmetric gauge theory recently discovered by Gaiotto and Witten. The model depends on a gauge group G and a hyper-Kaehler manifold X with a tri-holomorphic action of G. In the case when X is an affine space, we show that the model is equivalent to Chern-Simons theory whose gauge group is a supergroup. This explains the role of Lie superalgebras in the construction of Gaiotto and Witten. For general X, our model appears to be new. We describe some of its properties, focusing on the case when G is simple and X is the cotangent bundle of the flag variety of G. In particular, we show that Wilson loops are labeled by objects of a certain category which is a quantum deformation of the equivariant derived category of coherent sheaves on X.
Chern-Simons theory, 2d Yang-Mills, and Lie algebra wanderers
International Nuclear Information System (INIS)
Haro, Sebastian de
2005-01-01
We work out the relation between Chern-Simons, 2d Yang-Mills on the cylinder, and Brownian motion. We show that for the unitary, orthogonal and symplectic groups, various observables in Chern-Simons theory on S 3 and lens spaces are exactly given by counting the number of paths of a Brownian particle wandering in the fundamental Weyl chamber of the corresponding Lie algebra. We construct a fermionic formulation of Chern-Simons on S 3 which allows us to identify the Brownian particles as B-model branes moving on a noncommutative two-sphere, and construct 1- and 2-matrix models to compute Brownian motion ensemble averages
Unification of gauge and gravity Chern-Simons theories in 3-D space-time
Energy Technology Data Exchange (ETDEWEB)
Saghir, Chireen A.; Shamseddine, Laurence W. [American University of Beirut, Physics Department, Beirut (Lebanon)
2017-11-15
Chamseddine and Mukhanov showed that gravity and gauge theories could be unified in one geometric construction provided that a metricity condition is imposed on the vielbein. In this paper we are going to show that by enlarging the gauge group we are able to unify Chern-Simons gauge theory and Chern-Simons gravity in 3-D space-time. Such a unification leads to the quantization of the coefficients for both Chern-Simons terms for compact groups but not for non-compact groups. Moreover, it leads to a topological invariant quantity of the 3-dimensional space-time manifold on which they are defined. (orig.)
Wilson loops in 3-dimensional N = 6 supersymmetric Chern-Simons theory and their string theory duals
International Nuclear Information System (INIS)
Drukker, Nadav; Plefka, Jan; Young, Donovan
2008-01-01
We study Wilson loops in the three-dimensional N = 6 supersymmetric Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena, that is conjectured to be dual to type IIA string theory on AdS 4 x CP 3 . We construct loop operators in the Chern-Simons theory which preserve 1/6 of the supercharges and calculate their expectation value up to 2-loop order at weak coupling. The expectation value at strong coupling is found by constructing the string theory duals of these operators. For low dimensional representations these are fundamental strings, for high dimensional representations these are D2-branes and D6-branes. In support of this identification we demonstrate that these string theory solutions match the symmetries, charges and the preserved supersymmetries of their Chern-Simons theory counterparts.
A Lie based 4-dimensional higher Chern-Simons theory
Zucchini, Roberto
2016-05-01
We present and study a model of 4-dimensional higher Chern-Simons theory, special Chern-Simons (SCS) theory, instances of which have appeared in the string literature, whose symmetry is encoded in a skeletal semistrict Lie 2-algebra constructed from a compact Lie group with non discrete center. The field content of SCS theory consists of a Lie valued 2-connection coupled to a background closed 3-form. SCS theory enjoys a large gauge and gauge for gauge symmetry organized in an infinite dimensional strict Lie 2-group. The partition function of SCS theory is simply related to that of a topological gauge theory localizing on flat connections with degree 3 second characteristic class determined by the background 3-form. Finally, SCS theory is related to a 3-dimensional special gauge theory whose 2-connection space has a natural symplectic structure with respect to which the 1-gauge transformation action is Hamiltonian, the 2-curvature map acting as moment map.
Lorentz-violating Yang-Mills theory. Discussing the Chern-Simons-like term generation
Energy Technology Data Exchange (ETDEWEB)
Santos, Tiago R.S.; Sobreiro, Rodrigo F. [UFF-Universidade Federal Fluminense, Instituto de Fisica, Niteroi, RJ (Brazil)
2017-12-15
We analyze the Chern-Simons-like term generation in the CPT-odd Lorentz-violating Yang-Mills theory interacting with fermions. Moreover, we study the anomalies of this model as well as its quantum stability. The whole analysis is performed within the algebraic renormalization theory, which is independent of the renormalization scheme. In addition, all results are valid to all orders in perturbation theory. We find that the Chern-Simons-like term is not generated by radiative corrections, just like its Abelian version. Additionally, the model is also free of gauge anomalies and quantum stable. (orig.)
Self-dual Maxwell-Chern-Simons theory on a cylinder
International Nuclear Information System (INIS)
Han, Jongmin; Kim, Seongtag
2011-01-01
In this paper, we study the relativistic Maxwell-Chern-Simons vortices on an asymptotically flat cylinder. A topological multivortex solution is constructed by variational methods, and the Maxwell and the Chern-Simons limits are verified.
Entanglement from topology in Chern-Simons theory
Salton, Grant; Swingle, Brian; Walter, Michael
2017-05-01
The way in which geometry encodes entanglement is a topic of much recent interest in quantum many-body physics and the AdS/CFT duality. This relation is particularly pronounced in the case of topological quantum field theories, where topology alone determines the quantum states of the theory. In this work, we study the set of quantum states that can be prepared by the Euclidean path integral in three-dimensional Chern-Simons theory. Specifically, we consider arbitrary three-manifolds with a fixed number of torus boundaries in both Abelian U (1 ) and non-Abelian S O (3 ) Chern-Simons theory. For the Abelian theory, we find that the states that can be prepared coincide precisely with the set of stabilizer states from quantum information theory. This constrains the multipartite entanglement present in this theory, but it also reveals that stabilizer states can be described by topology. In particular, we find an explicit expression for the entanglement entropy of a many-torus subsystem using only a single replica, as well as a concrete formula for the number of GHZ states that can be distilled from a tripartite state prepared through path integration. For the non-Abelian theory, we find a notion of "state universality," namely that any state can be prepared to an arbitrarily good approximation. The manifolds we consider can also be viewed as toy models of multiboundary wormholes in AdS/CFT.
Holographic Chern-Simons defects
International Nuclear Information System (INIS)
Fujita, Mitsutoshi; Melby-Thompson, Charles M.; Meyer, René; Sugimoto, Shigeki
2016-01-01
We study SU(N) Yang-Mills-Chern-Simons theory in the presence of defects that shift the Chern-Simons level from a holographic point of view by embedding the system in string theory. The model is a D3-D7 system in Type IIB string theory, whose gravity dual is given by the AdS soliton background with probe D7 branes attaching to the AdS boundary along the defects. We holographically renormalize the free energy of the defect system with sources, from which we obtain the correlation functions for certain operators naturally associated to these defects. We find interesting phase transitions when the separation of the defects as well as the temperature are varied. We also discuss some implications for the Fractional Quantum Hall Effect and for 2-dimensional QCD.
Vortex solutions of a Maxwell-Chern-Simons field coupled to four-fermion theory
International Nuclear Information System (INIS)
Hyun, S.; Shin, J.; Yee, J.H.; Lee, H.
1997-01-01
We find the static vortex solutions of the model of a Maxwell-Chern-Simons gauge field coupled to a (2+1)-dimensional four-fermion theory. Especially, we introduce two matter currents coupled to the gauge field minimally: the electromagnetic current and a topological current associated with the electromagnetic current. Unlike other Chern-Simons solitons the N-soliton solution of this theory has binding energy and the stability of the solutions is maintained by the charge conservation laws. copyright 1997 The American Physical Society
The dynamical structure of higher dimensional Chern-Simons theory
International Nuclear Information System (INIS)
Banados, M.; Garay, L.J.; Henneaux, M.
1996-01-01
Higher dimensional Chern-Simons theories, even though constructed along the same topological pattern as in 2+1 dimensions, have been shown recently to have generically a non-vanishing number of degrees of freedom. In this paper, we carry out the complete Dirac Hamiltonian analysis (separation of first and second class constraints and calculation of the Dirac bracket) for a group G x U(1). We also study the algebra of surface charges that arise in the presence of boundaries and show that it is isomorphic to the WZW 4 discussed in the literature. Some applications are then considered. It is shown, in particular, that Chern-Simons gravity in dimensions greater than or equal to five has a propagating torsion. (orig.)
Chern-Simons invariants on hyperbolic manifolds and topological quantum field theories
Energy Technology Data Exchange (ETDEWEB)
Bonora, L. [International School for Advanced Studies (SISSA/ISAS), Trieste (Italy); INFN, Sezione di Trieste (Italy); Bytsenko, A.A.; Goncalves, A.E. [Universidade Estadual de Londrina, Departamento de Fisica, Londrina-Parana (Brazil)
2016-11-15
We derive formulas for the classical Chern-Simons invariant of irreducible SU(n)-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic physical principles). We show that a connection between holomorphic values of Selberg-type functions at point zero, associated with R-torsion of the flat bundle, and twisted Dirac operators acting on negatively curved manifolds, can be interpreted by means of the Chern-Simons invariant. On the basis of the Labastida-Marino-Ooguri-Vafa conjecture we analyze a representation of the Chern-Simons quantum partition function (as a generating series of quantum group invariants) in the form of an infinite product weighted by S-functions and Selberg-type functions. We consider the case of links and a knot and use the Rogers approach to discover certain symmetry and modular form identities. (orig.)
Physically meaningful and not so meaningful symmetries in Chern-Simons theory
International Nuclear Information System (INIS)
Giavarini, G.
1993-01-01
We explicitly show that the Landau gauge supersymmetry of Chern-Simons theory does not have any physical significance. In fact, the difference between an effective action both BRS invariant and Landau supersymmetric and an effective action only BRS invariant is a finite field redefinition. Having established this, we use a BRS invariant regulator that defines CS theory as the large mass limit of topologically massive Yang-Mills theory to discuss the shift k → k + c v of the bare Chern-Simons parameter k in connection with the Landau supersymmetry. Finally, to convince ourselves that the shift above is not an accident of our regularization method, we comment on the fact that all BRS invariant regulators used as yet yield the same value for the shift. (orig.)
SU(2) Chern-Simons theory at genus zero
International Nuclear Information System (INIS)
Gawedzki, K.; Kupiainen, A.
1991-01-01
We present a detailed study of the Schroedinger picture space of states in the SU(2) Chern-Simons topological gauge theory in the simplest geometry. The space coincides with that of the solutions of the chiral Ward identities for the WZW model. We prove that its dimension is given by E. Verlinde's formulae. (orig.)
Chern-Simons Theory, Matrix Models, and Topological Strings
International Nuclear Information System (INIS)
Walcher, J
2006-01-01
This book is a find. Marino meets the challenge of filling in less than 200 pages the need for an accessible review of topological gauge/gravity duality. He is one of the pioneers of the subject and a clear expositor. It is no surprise that reading this book is a great pleasure. The existence of dualities between gauge theories and theories of gravity remains one of the most surprising recent discoveries in mathematical physics. While it is probably fair to say that we do not yet understand the full reach of such a relation, the impressive amount of evidence that has accumulated over the past years can be regarded as a substitute for a proof, and will certainly help to delineate the question of what is the most fundamental quantum mechanical theory. Here is a brief summary of the book. The journey begins with matrix models and an introduction to various techniques for the computation of integrals including perturbative expansion, large-N approximation, saddle point analysis, and the method of orthogonal polynomials. The second chapter, on Chern-Simons theory, is the longest and probably the most complete one in the book. Starting from the action we meet Wilson loop observables, the associated perturbative 3-manifold invariants, Witten's exact solution via the canonical duality to WZW models, the framing ambiguity, as well as a collection of results on knot invariants that can be derived from Chern-Simons theory and the combinatorics of U (∞) representation theory. The chapter also contains a careful derivation of the large-N expansion of the Chern-Simons partition function, which forms the cornerstone of its interpretation as a closed string theory. Finally, we learn that Chern-Simons theory can sometimes also be represented as a matrix model. The story then turns to the gravity side, with an introduction to topological sigma models (chapter 3) and topological string theory (chapter 4). While this presentation is necessarily rather condensed (and the beginner may
Absence of higher order corrections to noncommutative Chern-Simons coupling
International Nuclear Information System (INIS)
Das, Ashok; Sheikh-Jabbari, M.M.
2001-03-01
We analyze the structure of noncommutative pure Chern-Simons theory systematically in the axial gauge. We show that there is no IR/UV mixing in this theory in this gauge. In fact, we show, using the usual BRST identities as well as the identities following from vector supersymmetry, that this is a free theory. As a result, the tree level Chern-Simons coefficient is not renormalized. It also holds that the Chern-Simons coefficient is not modified at finite temperature. (author)
Chern-Simons term at finite density and temperature
International Nuclear Information System (INIS)
Sisakyan, A.N.; Shevchenko, O.Yu.; Solganik, S.B.
1997-01-01
The Chern-Simons topological term dynamical generation in the effective action is obtained at arbitrary finite density and temperature. By using the proper time method and perturbation theory it is shown that at zero temperature μ 2 = m 2 is the crucial point for Chern-Simons term. So when μ 2 2 , μ influence disappears and we get the usual Chern-Simons term. On the other hand, when μ 2 > m 2 , the Chern-Simons term vanishes because of nonzero density of background fermions. In particular for massless case parity anomaly is absent at any finite density or temperature. This result holds in any odd dimension both in Abelian and in non-Abelian cases
Soliton condensation in some self-dual Chern-Simons theories
International Nuclear Information System (INIS)
Olesen, P.
1991-05-01
We show that the gauged non-linear Schroedinger equation has a closely packed soliton-condensate as a solution. We also show that the abelian Chern-Simons Higgs theory has a vortex condensate as an approximate solution whent he vortex cells are very small. (orig.)
Kaehler-Chern-Simons theory and symmetries of anti-self-dual gauge fields
International Nuclear Information System (INIS)
Nair, V.P.; Schiff, J.
1992-01-01
Kaehler-Chern-Simons theory, which was proposed as a generalization of ordinary Chern-Simons theory, is explored in more detail. The theory describes anti-self-dual instantons on a four-dimensional Kaehler manifold. The phase space is the space of gauge potentials, whose symplectic reduction by the constraints of anti-self-duality leads to the moduli space of instantons. We show that infinitesimal Baecklund transformations, previously related to 'hidden symmetries' of instantons, are canonical transformations generated by the anti-self-duality constraints. The quantum wave functions naturally lead to a generalized Wess-Zumino-Witten action, which in turn has associated chiral current algebras. The dimensional reduction of the anti-self-duality equations leading to integrable two-dimensional theories is briefly discussed in this framework. (orig.)
Friedan-Shenker bundle from Chern-Simons theory
International Nuclear Information System (INIS)
Falceto, F.
1990-01-01
In this letter we present a proof of the invariance of the space of quantum states of the Chern-Simons (CS) theory in the presence of Wilson lines under parallel transport with respect to the Knizhnik-Zamolodchikov (KZ) connection for the case of a simple, simply connected, finite-dimensional group and genus-zero surface. The proof is based on the polynomial realization of the space of tensors in which these quantum states take values. (orig.)
Non-existence of natural states for Abelian Chern-Simons theory
Dappiaggi, Claudio; Murro, Simone; Schenkel, Alexander
2017-06-01
We give an elementary proof that Abelian Chern-Simons theory, described as a functor from oriented surfaces to C∗-algebras, does not admit a natural state. Non-existence of natural states is thus not only a phenomenon of quantum field theories on Lorentzian manifolds, but also of topological quantum field theories formulated in the algebraic approach.
Transgression forms and extensions of Chern-Simons gauge theories
International Nuclear Information System (INIS)
Mora, Pablo; Olea, Rodrigo; Troncoso, Ricardo; Zanelli, Jorge
2006-01-01
A gauge invariant action principle, based on the idea of transgression forms, is proposed. The action extends the Chern-Simons form by the addition of a boundary term that makes the action gauge invariant (and not just quasi-invariant). Interpreting the spacetime manifold as cobordant to another one, the duplication of gauge fields in spacetime is avoided. The advantages of this approach are particularly noticeable for the gravitation theory described by a Chern-Simons lagrangian for the AdS group, in which case the action is regularized and finite for black hole geometries in diverse situations. Black hole thermodynamics is correctly reproduced using either a background field approach or a background-independent setting, even in cases with asymptotically nontrivial topologies. It is shown that the energy found from the thermodynamic analysis agrees with the surface integral obtained by direct application of Noether's theorem
Analysis of observables in Chern-Simons perturbation theory
International Nuclear Information System (INIS)
Alvarez, M.; Labastida, J.M.F.
1993-01-01
Chern-Simons theory with gauge group SU(N) is analyzed from a perturbation theory point of view. Computations up to order g 6 of the vacuum expectation value of the unknot are carried out and it is shown that agreement with the exact result by Witten implies no quantum correction at two loops for the two-point function. In addition, it is shown from a perturbation theory point of view that the framing dependence of the vacuum expectation value of an arbitrary knot factorizes in the form predicted by Witten. (orig.)
A profusion of 1/2 BPS Wilson loops in N=4 Chern-Simons-matter theories
International Nuclear Information System (INIS)
Cooke, Michael; Drukker, Nadav; Trancanelli, Diego
2015-01-01
We initiate the study of 1/2 BPS Wilson loops in N=4 Chern-Simons-matter theories in three dimensions. We consider a circular or linear quiver with Chern-Simons levels k, −k and 0, and focus on loops preserving one of the two SU(2) subgroups of the R-symmetry. In the cases with no vanishing Chern-Simons levels, we find a pair of Wilson loops for each pair of adjacent nodes on the quiver connected by a hypermultiplet (nodes connected by twisted hypermultiplets have Wilson loops preserving another set of supercharges). We expect this classical pairwise degeneracy to be lifted by quantum corrections. In the case with nodes with vanishing Chern-Simons terms connected by twisted hypermultiplets, we find that the usual 1/4 BPS Wilson loops are automatically enlarged to 1/2 BPS, as happens also in 3-dimensional Yang-Mills theory. When the nodes with vanishing Chern-Simons levels are connected by untwisted hypermultiplets, we do not find any Wilson loops coupling to those nodes which are classically invariant. Rather, we find several loops whose supersymmetry variation, while non zero, vanishes in any correlation function, so is weakly zero. We expect only one linear combination of those Wilson loops to remain BPS when quantum corrections are included. We analyze the M-theory duals of those Wilson loops and comment on their degeneracy. We also show that these Wilson loops are cohomologically equivalent to certain 1/4 BPS Wilson loops whose expectation value can be evaluated by the appropriate localized matrix model.
International Nuclear Information System (INIS)
Ezawa, Z.F.; Iwazaki, A.
1991-01-01
It is shown that Chern-Simons gauge theories describe both the fractional-quantum-Hall-effect (FQHE) hierarchy and anyon superconductivity, simply by field-theoretically extracting the effects of vortex excitations. Vortices correspond to Laughlin's quasiparticles or bound states of anyons. Both of these phenomena are explained by the condensations of these vortices. We clarify why the anyon systems become incompressible (FQHE) or compressible (anyon superconductivity) depending on the statistics. It is to be emphasized that we can derive an effective Lagrangian describing fully the FQHE hierarchy from a basic Chern-Simons gauge theory
Super-Chern-Simons Theory as Superstring Theory
Grassi, P A
2004-01-01
Superstrings and topological strings with supermanifolds as target space play a central role in the recent developments in string theory. Nevertheless the rules for higher-genus computations are still unclear or guessed in analogy with bosonic and fermionic strings. Here we present a common geometrical setting to develop systematically the prescription for amplitude computations. The geometrical origin of these difficulties is the theory of integration of superforms. We provide a translation between the theory of supermanifolds and topological strings with supertarget space. We show how in this formulation one can naturally construct picture changing operators to be inserted in the correlation functions to soak up the zero modes of commuting ghost and we derive the amplitude prescriptions from the coupling with an extended topological gravity on the worldsheet. As an application we consider a simple model on R^(3|2) leading to super-Chern-Simons theory.
Supersymmetry, quantum gauge anomalies and generalized Chern-Simons terms in chiral gauge theory
International Nuclear Information System (INIS)
Schmidt, Torsten
2009-01-01
The purpose of this thesis is to investigate the interplay of anomaly cancellation and generalized Chern-Simons terms in four-dimensional chiral gauge theory. We start with a detailed discussion of generalized Chern-Simons terms with the canellation of anomalies via the Green-Schwarz mechanism. With this at hand, we investigate the situation in general N=1 supersymmetric field theories with generalized Chern-Simons terms. Two simple consistency conditions are shown to encode strong constraints on the allowed anomalies for different types of gauge groups. In one major part of this thesis we are going to display to what extent one has to modify the existing formalism in order to allow for the cancellation of quantum gauge anomalies via the Green-Schwarz mechanism. At the end of this thesis we comment on a puzzle in the literature on supersymmetric field theories with massive tensor fields. The potential contains a term that does not arise from eliminating an auxiliary field. We clarify the origin of this term and display the relation to standard D-term potential. In an appendix it is explicitly shown how these low energy effective actions might be connected to the formulation of four-dimensional gauge theories discussed at earlier stages of this thesis. (orig.)
Castro \\C
2003-01-01
Moyal noncommutative star-product deformations of higher dimensional gravitational Einstein-Hilbert actions via lower-dimensional SU(\\infty) gauge theories are constructed explicitly based on the holographic reduction principle. New reparametrization invariant p-brane actions and their Moyal star product deformations follows. It is conjectured that topological Chern-Simons brane actions associated with higher-dimensional "knots" have a one-to-one correspondence with topological Chern-Simons Matrix models in the large N limit. The corresponding large N limit of Topological BF Matrix models leads to Kalb-Ramond couplings of antisymmetric-tensor fields to p-branes. The former Chern-Simons branes display higher-spin W_\\infty symmetries which are very relevant in the study of W_\\infty Gravity, the Quantum Hall effect and its higher-dimensional generalizations. We conclude by arguing why this interplay between condensed matter models, higher-dimensional extensions of the Quantum Hall effect, Chern-Simons Matrix mod...
The Chern-Simons diffusion rate in improved holographic QCD
Gürsoy, U.; Iatrakis, I.; Kiritsis, E.; Nitti, F.; O’Bannon, A.
2013-01-01
In (3 + 1)-dimensional SU(N c) Yang-Mills (YM) theory, the Chern-Simons diffusion rate, ΓCS, is determined by the zero-momentum, zero-frequency limit of the retarded two-point function of the CP-odd operator tr [F ∧ F ], with F the YM field strength. The Chern-Simons diffusion rate is a crucial
Chern-Simons terms and cocycles in physics and mathematics
Energy Technology Data Exchange (ETDEWEB)
Jackiw, R.
1984-12-01
Contemporary topological research in Yang-Mills theory is reviewed, emphasizing the Chern-Simons terms and their relatives. Three applications of the Chern-Simons terms in physical theory are described: to help understanding gauge theories in even dimensional space-time; gauge field dynamics in odd dimensional space-time; and mathematically coherent description of even-dimensional gauge theories with chiral fermions that are apparently inconsistent due to chiral anomalies. Discussion of these applications is preceded by explanation of the mathematical preliminaries and examples in simple quantum mechanical settings. 24 refs. (LEW)
Introductory lectures on Chern-Simons theories
Zanelli, Jorge
2012-02-01
The Chern-Simons (CS) form evolved from an obstruction in mathematics into an important object in theoretical physics. In fact, the presence of CS terms in physics is more common than one may think. They are found in the studies of anomalies in quantum field theories and as Lagrangians for gauge fields, including gravity and supergravity. They seem to play an important role in high Tc superconductivity and in recently discovered topological insulators. CS forms are also the natural generalization of the minimal coupling between the electromagnetic field and a point charge when the source is not point-like but an extended fundamental object, a membrane. A cursory review of these ideas is presented at an introductory level.
Dynamics of Chern-Simons vortices
International Nuclear Information System (INIS)
Collie, Benjamin; Tong, David
2008-01-01
We study vortex dynamics in three-dimensional theories with Chern-Simons interactions. The dynamics is governed by motion on the moduli space M in the presence of a magnetic field. For Abelian vortices, the magnetic field is shown to be the Ricci form over M; for non-Abelian vortices, it is the first Chern character of a suitable index bundle. We derive these results by integrating out massive fermions and following the fate of their zero modes.
International Nuclear Information System (INIS)
Chen Famin; Wu Yongshi
2010-01-01
We present a superspace formulation of the D=3, N=4, 5 superconformal Chern-Simons Matter theories, with matter supermultiplets valued in a symplectic 3-algebra. We first construct an N=1 superconformal action and then generalize a method used by Gaitto and Witten to enhance the supersymmetry from N=1 to N=5. By decomposing the N=5 supermultiplets and the symplectic 3-algebra properly and proposing a new superpotential term, we construct the N=4 superconformal Chern-Simons matter theories in terms of two sets of generators of a (quaternion) symplectic 3-algebra. The N=4 theories can also be derived by requiring that the supersymmetry transformations are closed on-shell. The relationship between the 3-algebras, Lie superalgebras, Lie algebras, and embedding tensors (proposed in [E. A. Bergshoeff, O. Hohm, D. Roest, H. Samtleben, and E. Sezgin, J. High Energy Phys. 09 (2008) 101.]) is also clarified. The general N=4, 5 superconformal Chern-Simons matter theories in terms of ordinary Lie algebras can be re-derived in our 3-algebra approach. All known N=4, 5 superconformal Chern-Simons matter theories can be recovered in the present superspace formulation for super-Lie algebra realization of symplectic 3-algebras.
Chern-Simons matrix models and unoriented strings
International Nuclear Information System (INIS)
Halmagyi, Nick; Yasnov, Vadim
2004-01-01
For matrix models with measure on the Lie algebra of SO/Sp, the sub-leading free energy is given by F 1 (S) ±{1/4}({δF 0 (S)}/{δS}). Motivated by the fact that this relationship does not hold for Chern-Simons theory on S 3 , we calculate the sub-leading free energy in the matrix model for this theory, which is a Gaussian matrix model with Haar measure on the group SO/Sp. We derive a quantum loop equation for this matrix model and then find that F 1 is an integral of the leading order resolvent over the spectral curve. We explicitly calculate this integral for quadratic potential and find agreement with previous studies of SO/Sp Chern-Simons theory. (author)
A Chern-Simons-like action for closed-string field theory
International Nuclear Information System (INIS)
Taylor, C.C.
1989-01-01
A Chern-Simons-like action is proposed for closed-string field theory. The action involves auxiliary fields of arbitrary ghost number and is defined in terms of the closed-string operations ∫, Q and *, analogous to those introduced by Witten in the construction of open-string field theory. The action is an extension of one proposed for free closed strings and bears a formal relationship to 2 + 1 gravity analogous to that between open-string field theory and (2 + 1)-dimensional Yang-Mills theory. (author)
Composite Chern-Simons gauge boson in anyon gas
International Nuclear Information System (INIS)
Nguyen Van Hieu; Nguyen Hung Son.
1990-08-01
It was shown that in a free anyon gas there exists a composite vector gauge field with the effective action containing a Chern-Simons term. The momentum dependence of the energy of the composite boson was found. The mixing between Chern-Simons boson and photon gives rise to the appearance of new quasiparticles - Chern-Simons polaritons. The dispersion equations of Chern-Simons polaritons were derived. (author). 14 refs
Chern-Simons couplings for dielectric F-strings in matrix string theory
International Nuclear Information System (INIS)
Brecher, Dominic; Janssen, Bert; Lozano, Yolanda
2002-01-01
We compute the non-abelian couplings in the Chern-Simons action for a set of coinciding fundamental strings in both the type IIA and type IIB Matrix string theories. Starting from Matrix theory in a weakly curved background, we construct the linear couplings of closed string fields to type IIA Matrix strings. Further dualities give a type IIB Matrix string theory and a type IIA theory of Matrix strings with winding. (Abstract Copyright[2002], Wiley Periodicals, Inc.)
Chern-Simons forms in gravitation theories
International Nuclear Information System (INIS)
Zanelli, Jorge
2012-01-01
The Chern-Simons (CS) form evolved from an obstruction in mathematics into an important object in theoretical physics. In fact, the presence of CS terms in physics is more common than one may think: they seem to play an important role in high Tc superconductivity and in recently discovered topological insulators. In classical physics, the minimal coupling in electromagnetism and to the action for a mechanical system in Hamiltonian form are examples of CS functionals. CS forms are also the natural generalization of the minimal coupling between the electromagnetic field and a point charge when the source is not point like but an extended fundamental object, a membrane. They are found in relation with anomalies in quantum field theories, and as Lagrangians for gauge fields, including gravity and supergravity. A cursory review of the role of CS forms in gravitation theories is presented at an introductory level. (topical review)
Chern-Simons forms in gravitation theories
Zanelli, Jorge
2012-07-01
The Chern-Simons (CS) form evolved from an obstruction in mathematics into an important object in theoretical physics. In fact, the presence of CS terms in physics is more common than one may think: they seem to play an important role in high Tc superconductivity and in recently discovered topological insulators. In classical physics, the minimal coupling in electromagnetism and to the action for a mechanical system in Hamiltonian form are examples of CS functionals. CS forms are also the natural generalization of the minimal coupling between the electromagnetic field and a point charge when the source is not point like but an extended fundamental object, a membrane. They are found in relation with anomalies in quantum field theories, and as Lagrangians for gauge fields, including gravity and supergravity. A cursory review of the role of CS forms in gravitation theories is presented at an introductory level.
Skein relations and Wilson loops in Chern-Simons gauge theory
International Nuclear Information System (INIS)
Horne, J.H.
1990-01-01
We derive the skein relations for the fundamental representations of SO(N), Sp(2n), SU(mvertical stroken), and OSp(mvertical stroke2n). These relations can be used recursively to calculate the expectation values of Wilson lines in three-dimensional Chern-Simons gauge theory with these gauge groups. A combination of braiding and tying of Wilson lines completely describes the skein relations. (orig.)
Two-dimensional Lorentz-Weyl anomaly and gravitational Chern-Simons theory
International Nuclear Information System (INIS)
Chamseddine, A.H.; Froehlich, J.
1992-01-01
Two-dimensional chiral fermions and bosons, more generally conformal blocks of two-dimensional conformal field theories, exhibit Weyl-, Lorentz- and mixed Lorentz-Weyl anomalies. A novel way of computing these anomalies for a system of chiral bosons of arbitrary conformal spin j is sketched. It is shown that the Lorentz- and mixed Lorentz-Weyl anomalies of these theories can be cancelled by the anomalies of a three-dimensional classical Chern-Simons action for the spin connection, expressed in terms of the dreibein field. Some tentative applications of this result to string theory are indicated. (orig.)
Instantons, fermions and Chern-Simons terms
International Nuclear Information System (INIS)
Collie, Benjamin; Tong, David
2008-01-01
In five spacetime dimensions, instantons are finite energy, solitonic particles. We describe the dynamics of these objects in the presence of a Chern-Simons interaction. For U(N) instantons, we show that the 5d Chern-Simons term induces a corresponding Chern-Simons term in the ADHM quantum mechanics. For SU(N) instantons, we provide a description in terms of geodesic motion on the instanton moduli space, modified by the presence of a magnetic field. We show that this magnetic field is equal to the first Chern character of an index bundle. All of these results are derived by a simple method which follows the fate of zero modes as fermions are introduced, made heavy, and subsequently integrated out.
Abelian Chern endash Simons theory. II. A functional integral approach
International Nuclear Information System (INIS)
Manoliu, M.
1998-01-01
Following Witten, [Commun. Math. Phys. 21, 351 endash 399 (1989)] we approach the Abelian quantum Chern endash Simons (CS) gauge theory from a Feynman functional integral point of view. We show that for 3-manifolds with and without a boundary the formal functional integral definitions lead to mathematically proper expressions that agree with the results from the rigorous construction [J. Math. Phys. 39, 170 endash 206 (1998)] of the Abelian CS topological quantum field theory via geometric quantization. copyright 1998 American Institute of Physics
Embedded graph invariants in Chern-Simons theory
International Nuclear Information System (INIS)
Major, Seth A.
1999-01-01
Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants. In this work the theory is used to explore the definition of the expectation value of a network of Wilson lines -- an embedded graph invariant. Using a generalization of the variational method, lowest-order results for invariants for graphs of arbitrary valence and general vertex tangent space structure are derived. Gauge invariant operators are introduced. Higher order results are found. The method used here provides a Vassiliev-type definition of graph invariants which depend on both the embedding of the graph and the group structure of the gauge theory. It is found that one need not frame individual vertices. However, without a global projection of the graph there is an ambiguity in the relation of the decomposition of distinct vertices. It is suggested that framing may be seen as arising from this ambiguity -- as a way of relating frames at distinct vertices
Garoufalidis, S; Garoufalidis, Stavros; Marino, Marcos
2006-01-01
The contribution of reducible connections to the U(N) Chern-Simons invariant of a Seifert manifold $M$ can be expressed in some cases in terms of matrix integrals. We show that the U(N) evaluation of the LMO invariant of any rational homology sphere admits a matrix model representation which agrees with the Chern-Simons matrix integral for Seifert spheres and the trivial connection.
The integral form of D = 3 Chern-Simons theories probing C{sup n}/Γ singularities
Energy Technology Data Exchange (ETDEWEB)
Fre, P. [Dipartimento di Fisica, Universita di Torino (Italy); INFN - Sezione di Torino (Italy); Arnold-Regge Center, Torino (Italy); National Research Nuclear University MEPhI, (Moscow Engineering Physics Institute), Moscow (Russian Federation); Grassi, P.A. [INFN - Sezione di Torino (Italy); Arnold-Regge Center, Torino (Italy); DISIT, Universita del Piemonte Orientale, Alessandria (Italy); Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University (Japan)
2017-10-15
We consider D=3 supersymmetric Chern Simons gauge theories both from the point of view of their formal structure and of their applications to the AdS{sub 4}/CFT{sub 3} correspondence. From the structural view-point, we use the new formalism of integral forms in superspace that utilizes the rheonomic Lagrangians and the Picture Changing Operators, as an algorithmic tool providing the connection between different approaches to supersymmetric theories. We provide here the generalization to an arbitrary Kaehler manifold with arbitrary gauge group and arbitrary superpotential of the rheonomic lagrangian of D=3 matter coupled gauge theories constructed years ago. From the point of view of the AdS{sub 4}/CFT{sub 3} correspondence and more generally of M2-branes we emphasize the role of the Kaehler quotient data in determining the field content and the interactions of the Cherns Simons gauge theory when the transverse space to the brane is a non-compact Kaehler quotient K{sub 4} of some flat variety with respect to a suitable group. The crepant resolutions of C{sup n}/Γ singularities fall in this category. In the present paper we anticipate the general scheme how the geometrical data are to be utilized in the construction of the D=3 Chern-Simons Theory supposedly dual to the corresponding M2-brane solution. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
On eleven-dimensional supergravity and Chern-Simons theory
Energy Technology Data Exchange (ETDEWEB)
Izaurieta, Fernando, E-mail: fizaurie@ucsc.cl [Departamento de Matematica y Fisica Aplicadas, Universidad Catolica de la Santisima Concepcion, Alonso de Ribera 2850, 4090541 Concepcion (Chile); Instituto de Matematicas, Universidad Nacional Autonoma de Mexico, Av. Insurgentes Sur s/n, D.F. (Mexico); Departament de Fisica Teorica, Universitat de Valencia, C/ Dr. Moliner 50, 46100 Burjassot, Valencia (Spain); Rodriguez, Eduardo, E-mail: edurodriguez@ucsc.cl [Departamento de Matematica y Fisica Aplicadas, Universidad Catolica de la Santisima Concepcion, Alonso de Ribera 2850, 4090541 Concepcion (Chile)
2012-02-11
We probe in some depth into the structure of eleven-dimensional, osp(32|1)-based Chern-Simons supergravity, as put forward by Troncoso and Zanelli (TZ) in 1997. We find that the TZ Lagrangian may be cast as a polynomial in 1/l, where l is a length, and compute explicitly the first three dominant terms. The term proportional to 1/l{sup 9} turns out to be essentially the Lagrangian of the standard 1978 supergravity theory of Cremmer, Julia and Scherk, thus establishing a previously unknown relation between the two theories. The computation is nontrivial because, when written in a sufficiently explicit way, the TZ Lagrangian has roughly one thousand non-explicitly Lorentz-covariant terms. Specially designed algebraic techniques are used to accomplish the results.
Integrable spin chain of superconformal U(M) x U(N)-bar Chern-Simons theory
International Nuclear Information System (INIS)
Bak, Dongsu; Gang, Dongmin; Rey, Soo-Jong
2008-01-01
N = 6 superconformal Chern-Simons theory with gauge group U(M) x U(N)-bar is dual to N M2-branes and (M-N) fractional M2-branes, equivalently, discrete 3-form holonomy at C 4 /Z k orbifold singularity. We show that, much like its regular counterpart of M = N, the theory at planar limit have integrability structure in the conformal dimension spectrum of single trace operators. We first revisit the Yang-Baxter equation for a spin chain system associated with the single trace operators. We show that the integrability by itself does not preclude parity symmetry breaking. We construct two-parameter family of parity non-invariant, alternating spin chain Hamiltonian involving three-site interactions between 4 and 4-bar of SU(4) R . At weak 't Hooft coupling, we study the Chern-Simons theory perturbatively and calculate anomalous dimension of single trace operators up to two loops. The computation is essentially parallel to the regular case M = N. We find that resulting spin chain Hamiltonian matches with the Hamiltonian derived from Yang-Baxter equation, but to the one preserving parity symmetry. We give several intuitive explanations why the parity symmetry breaking is not detected in the Chern-Simons spin chain Hamiltonian at perturbative level. We suggest that open spin chain, associated with open string excitations on giant gravitons or dibaryons, can detect discrete flat holonomy and hence parity symmetry breaking through boundary field.
Even-dimensional topological gravity from Chern-Simons gravity
International Nuclear Information System (INIS)
Merino, N.; Perez, A.; Salgado, P.
2009-01-01
It is shown that the topological action for gravity in 2n-dimensions can be obtained from the (2n+1)-dimensional Chern-Simons gravity genuinely invariant under the Poincare group. The 2n-dimensional topological gravity is described by the dynamics of the boundary of a (2n+1)-dimensional Chern-Simons gravity theory with suitable boundary conditions. The field φ a , which is necessary to construct this type of topological gravity in even dimensions, is identified with the coset field associated with the non-linear realizations of the Poincare group ISO(d-1,1).
Chern-Simons gauge theory: Ten years after
International Nuclear Information System (INIS)
Labastida, J. M. F.
1999-01-01
A brief review on the progress made in the study of Chern-Simons gauge theory since its relation to knot theory was discovered ten years ago is presented. Emphasis is made on the analysis of the perturbative study of the theory and its connection to the theory of Vassiliev invariants. It is described how the study of the quantum field theory for three different gauge fixings leads to three different representations for Vassiliev invariants. Two of these gauge fixings lead to well known representations: the covariant Landau gauge corresponds to the configuration space integrals while the non-covariant light-cone gauge to the Kontsevich integral. The progress made in the analysis of the third gauge fixing, the non-covariant temporal gauge, is described in detail. In this case one obtains combinatorial expressions, instead of integral ones, for Vassiliev invariants. The approach based on this last gauge fixing seems very promising to obtain a full combinatorial formula. We collect the combinatorial expressions for all the Vassiliev invariants up to order four which have been obtained in this approach
BRST Formalism in Self-Dual Chern-Simons Theory with Matter Fields
Dai, Jialiang; Fan, Engui
2018-04-01
We apply BRST method to the self-dual Chern-Simons gauge theory with matter fields and the generators of symmetries of the system from an elegant Lie algebra structure under the operation of Poisson bracket. We discuss four different cases: abelian, nonabelian, relativistic, and nonrelativistic situations and extend the system to the whole phase space including ghost fields. In addition, we obtain the BRST charge of the field system and check its nilpotence of the BRST transformation which plays an important role such as in topological quantum field theory and string theory.
Yang-Mills-Chern-Simons supergravity
International Nuclear Information System (INIS)
Lue, H; Pope, C N; Sezgin, E
2004-01-01
N = (1, 0) supergravity in six dimensions admits AdS 3 x S 3 as a vacuum solution. We extend our recent results presented in Lue et al (2002 Preprint hep-th/0212323), by obtaining the complete N = 4 Yang-Mills-Chern-Simons supergravity in D = 3, up to quartic fermion terms, by S 3 group manifold reduction of the six-dimensional theory. The SU(2) gauge fields have Yang-Mills kinetic terms as well as topological Chern-Simons mass terms. There is in addition a triplet of matter vectors. After diagonalization, these fields describe two triplets of topologically-massive vector fields of opposite helicities. The model also contains six scalars, described by a GL(3, R)/SO(3) sigma model. It provides the first example of a three-dimensional gauged supergravity that can be obtained by a consistent reduction of string theory or M-theory and that admits AdS 3 as a vacuum solution. There are unusual features in the reduction from six-dimensional supergravity, owing to the self-duality condition on the 3-form field. The structure of the full equations of motion in N = (1, 0) supergravity in D = 6 is also elucidated, and the role of the self-dual field strength as torsion is exhibited
Extended charged events and Chern-Simons couplings
International Nuclear Information System (INIS)
Bunster, Claudio; Gomberoff, Andres; Henneaux, Marc
2011-01-01
In three spacetime dimensions, the world volume of a magnetic source is a single point, a magnetically charged event. It has been shown long ago that in three-dimensional spacetime, the Chern-Simons coupling is quantized, because the magnetic event emits an electric charge which must be quantized according to the standard Dirac rule. Recently, the concept of dynamical extended charged events has been introduced, and it has been argued that they should play as central a role as that played by particles or ordinary branes. In this article, we show that in the presence of a Chern-Simons coupling, a magnetically charged extended event emits an extended object, which geometrically is just like a Dirac string, but it is observable, obeys equations of motion, and may be electrically charged. We write a complete action principle which accounts for this effect. The action involves two Chern-Simons terms, one integrated over spacetime and the other integrated over the world volume of the submanifold that is the union of the Dirac world sheet and the history of the emitted physical object. By demanding that the total charge emitted by a composite extended magnetic event be quantized according to Dirac's rule, we find a quantization condition for the Chern-Simons coupling. For a 1-form electric potential in D=2n+1 spacetime dimensions, the composite event is formed by n elementary extended magnetic events separated in time such that the product of their transverse spaces, together with the time axis, is the entire spacetime. We show that the emitted electric charge is given by the integral of the (n-1)-th exterior power of the electromagnetic field strength over the last elementary event, or, equivalently, over an appropriate closed surface. The extension to more general p-form potentials and higher dimensions is also discussed. For the case D=11, p=3, our result for the quantization of the Chern-Simons coupling was obtained previously in the context of M theory, an agreement
Maxwell-Chern-Simons theory in covariant and Coulomb gauges
International Nuclear Information System (INIS)
Haller, K.; Lim-Lombridas, E.
1996-01-01
We quantize quantum electrodynamics in 2 + 1 dimensions coupled to a Chern-Simons (CS) term and a charged spinor field, in covariant gauges and in the Coulomb gauge. The resulting Maxwell-Chern-Simons (MCS) theory describes charged fermions interacting with each other and with topologically massive propagating photons. We impose Gauss's law and the gauge conditions and investigate their effect on the dynamics and on the statistics of n-particle states. We construct charged spinor states that obey Gauss's law and the gauge conditions and transform the theory to representations in which these states constitute a Fock space. We demonstrate that, in these representations, the nonlocal interactions between charges and between charges and transverse currents-along with the interactions between currents and massive propagating photons-are identical in the different gauges we analyze in this and in earlier work. We construct the generators of the Poincare group, show that they implement the Poincare algebra, and explicitly demonstrate the effect of rotations and Lorentz boosts on the particle states. We show that the imposition of Gauss's law does not produce any open-quotes exoticclose quotes fractional statistics. In the case of the covariant gauges, this demonstration makes use of unitary transformations that provide charged particles with the gauge fields required by Gauss's law, but that leave the anticommutator algebra of the spinor fields untransformed. In the Coulomb gauge, we show that the anticommutators of the spinor fields apply to the Dirac-Bergmann constraint surfaces, on which Gauss's law and the gauge conditions obtain. We examine MCS theory in the large CS coupling constant limit, and compare that limiting form with CS theory, in which the Maxwell kinetic energy term is not included in the Larangian. 34 refs
Charges and Energy in Chern-Simons Theories and Lovelock Gravity
Allemandi, G.; Francaviglia, M.; Raiteri, M.
2003-01-01
Starting from the SO(2,2n) Chern-Simons form in (2n+1) dimensions we calculate the variation of conserved quantities in Lovelock gravity and Lovelock-Maxwell gravity through the covariant formalism developed in gr-qc/0305047. Despite the technical complexity of the Lovelock Lagrangian we obtain a remarkably simple expression for the variation of the charges ensuing from the diffeomorphism covariance of the theory. The viability of the result is tested in specific applications and the formal e...
Derivation of the Verlinde formula from Chern-Simons theory and the G/G model
International Nuclear Information System (INIS)
Blau, M.; Thompson, G.
1993-01-01
We give a derivation of the Verlinde formula for the G k WZW model from Chern-Simons theory, without taking recourse to CFT, by calculating explicitly the partition function Z ΣxS 1 of Σ x S 1 with an arbitrary number of labelled punctures. By what is essentially a suitable gauge choice, Z ΣxS 1 is reduced to the partition function of an abelian topological field theory on Σ (a deformation of non-abelian BF and Yang-Mills theory) whose evaluation is straightforward. This relates the Verlinde formula to the Ray-Singer torsion of Σ x S 1 . We derive the G k /G k model from Chern-Simons theory, proving their equivalence, and give an alternative derivation of the Verlinde formula by calculating the G k /G k path integral via a functional version of the Weyl integral formula. From this point of view the Verlinde formula arises from the corresponding jacobian, the Weyl determinant. Also, a novel derivation of the shift k → k + h is given, based on the index of the twisted Dolbeault complex. (orig.)
Maxwell-Chern-Simons Casimir effect
International Nuclear Information System (INIS)
Milton, K.A.; Ng, Y.J.
1990-01-01
The topology of (2+1)-dimensional space permits the construction of quantum electrodynamics with the usual Maxwell action augmented by a gauge-invariant, but P- and T-violating, Chern-Simons mass term. We discuss the Casimir effect between parallel lines in such a theory. The effect of finite temperature is also considered. In principle, our results provide a way to measure the topological mass of the photon
A flat Chern-Simons gauge theory for (2+1)-dimensional gravity coupled to point particles
International Nuclear Information System (INIS)
Grignani, G.; Nardelli, G.
1991-01-01
We present a classical ISO (2,1) Chern-Simons gauge theory for planar gravity coupled to point-like sources. The theory is defined in terms of flat coordinates whose relation with the space-time coordinates is established. Though flat, the theory is equivalent to Einstein's as we show explicitly in two examples. (orig.)
Chern-Simons theories of symplectic super-diffeomorphisms
International Nuclear Information System (INIS)
Sezgin, E.; Sokatchev, E.
1989-04-01
We discuss the symplectic diffeomorphisms of a class of supermanifolds and the structure of the underlying infinite dimensional superalgebras. We construct a Chern-Simons (CS) gauge theory in 2+1 dimensions for these algebras. There exists a finite dimensional supersymmetric truncation which is the (2 n -1)-dimensional Hamiltonian superalgebra H-tilde(n). With a central charge added, it is a superalgebra, C(n), associated with a Clifford algebra. We find an embedding of d=3, N=2 anti-de Sitter superalgebra OSp(2|2)+OSp(2|2) in C(4), and construct a CS action for its infinite dimensional extension. We also discuss the construction of a CS action for the infinite dimensional extension of the d=3, N=2 superconformal algebra OSp(2,4). (author). 18 refs
Dynamical Mass Generation and Confinement in Maxwell-Chern-Simons Planar Quantum Electrodynamics
International Nuclear Information System (INIS)
Sanchez Madrigal, S; Raya, A; Hofmann, C P
2011-01-01
We study the non-perturbative phenomena of Dynamical Mass Generation and Confinement by truncating at the non-perturbative level the Schwinger-Dyson equations in Maxwell-Chern-Simons planar quantum electrodynamics. We obtain numerical solutions for the fermion propagator in Landau gauge within the so-called rainbow approximation. A comparison with the ordinary theory without the Chern-Simons term is presented.
Pure Lovelock gravity and Chern-Simons theory
Concha, P. K.; Durka, R.; Inostroza, C.; Merino, N.; Rodríguez, E. K.
2016-07-01
We explore the possibility of finding pure Lovelock gravity as a particular limit of a Chern-Simons action for a specific expansion of the AdS algebra in odd dimensions. We derive in detail this relation at the level of the action in five and seven dimensions. We provide a general result for higher dimensions and discuss some issues arising from the obtained dynamics.
Perturbative expansion of Chern-Simons theory with non-compact gauge group
International Nuclear Information System (INIS)
Bar-Natan, D.; Witten, E.
1991-01-01
Naive imitation of the usual formulas for compact gauge group in quantizing three dimensional Chern-Simons gauge theory with non-compact gauge group leads to formulas that are wrong or unilluminating. In this paper, an appropriate modification is described, which puts the perturbative expansion in a standard manifestly 'unitary' format. The one loop contributions (which differ from naive extrapolation from the case of compact gauge group) are computed, and their topological invariance is verified. (orig.)
Exact solubility of Chern-Simons theory with compact simple gauge group
International Nuclear Information System (INIS)
Hayashi, Masahito
1993-01-01
We show that vacuum expectation values of Wilson loop operators in (2+1)-dimensional Chern-Simons theory satisfy algebraic equations. Interestingly enough, vacuum expectation values for unknotted Wilson loop operators in any representation of any compact and simple group are exactly computed by solving the equations. So-called 'skein relations', which give us algebraic equations among vacuum expectation values of different Wilson loop operators, are constructed. In our formalism, quantum group symmetry appears naturally. (orig.)
The Chern-Simons Current in Systems of DNA-RNA Transcriptions
Capozziello, Salvatore; Pincak, Richard; Kanjamapornkul, Kabin; Saridakis, Emmanuel N.
2018-04-01
A Chern-Simons current, coming from ghost and anti-ghost fields of supersymmetry theory, can be used to define a spectrum of gene expression in new time series data where a spinor field, as alternative representation of a gene, is adopted instead of using the standard alphabet sequence of bases $A, T, C, G, U$. After a general discussion on the use of supersymmetry in biological systems, we give examples of the use of supersymmetry for living organism, discuss the codon and anti-codon ghost fields and develop an algebraic construction for the trash DNA, the DNA area which does not seem active in biological systems. As a general result, all hidden states of codon can be computed by Chern-Simons 3 forms. Finally, we plot a time series of genetic variations of viral glycoprotein gene and host T-cell receptor gene by using a gene tensor correlation network related to the Chern-Simons current. An empirical analysis of genetic shift, in host cell receptor genes with separated cluster of gene and genetic drift in viral gene, is obtained by using a tensor correlation plot over time series data derived as the empirical mode decomposition of Chern-Simons current.
Mimetic discretization of the Abelian Chern-Simons theory and link invariants
Energy Technology Data Exchange (ETDEWEB)
Di Bartolo, Cayetano; Grau, Javier [Departamento de Física, Universidad Simón Bolívar, Apartado Postal 89000, Caracas 1080-A (Venezuela, Bolivarian Republic of); Leal, Lorenzo [Departamento de Física, Universidad Simón Bolívar, Apartado Postal 89000, Caracas 1080-A (Venezuela, Bolivarian Republic of); Centro de Física Teórica y Computacional, Facultad de Ciencias, Universidad Central de Venezuela, Apartado Postal 47270, Caracas 1041-A (Venezuela, Bolivarian Republic of)
2013-12-15
A mimetic discretization of the Abelian Chern-Simons theory is presented. The study relies on the formulation of a theory of differential forms in the lattice, including a consistent definition of the Hodge duality operation. Explicit expressions for the Gauss Linking Number in the lattice, which correspond to their continuum counterparts are given. A discussion of the discretization of metric structures in the space of transverse vector densities is presented. The study of these metrics could serve to obtain explicit formulae for knot an link invariants in the lattice.
Accelerated FRW solutions in Chern-Simons gravity
International Nuclear Information System (INIS)
Cataldo, Mauricio; Crisostomo, Juan; Gomez, Fernando; Salgado, Patricio; Campo, Sergio del; Quinzacara, Cristian C.
2014-01-01
We consider a five-dimensional Einstein-Chern-Simons action which is composed of a gravitational sector and a sector of matter where the gravitational sector is given by a Chern-Simons gravity action instead of the Einstein-Hilbert action and where the matter sector is given by the so-called perfect fluid. It is shown that (i) the Einstein-Chern-Simons (EChS) field equations subject to suitable conditions can be written in a similar way to the Einstein-Maxwell field equations; (ii) these equations have solutions that describe an accelerated expansion for the three possible cosmological models of the universe, namely, spherical expansion, flat expansion, and hyperbolic expansion when α a parameter of the theory, is greater than zero. This result allows us to conjecture that these solutions are compatible with the era of dark energy and that the energy-momentum tensor for the field h a , a bosonic gauge field from the Chern-Simons gravity action, corresponds to a form of positive cosmological constant. It is also shown that the EChS field equations have solutions compatible with the era of matter: (i) In the case of an open universe, the solutions correspond to an accelerated expansion (α > 0) with a minimum scale factor at initial time that, when time goes to infinity, the scale factor behaves as a hyperbolic sine function. (ii) In the case of a flat universe, the solutions describe an accelerated expansion whose scale factor behaves as an exponential function of time. (iii) In the case of a closed universe there is found only one solution for a universe in expansion, which behaves as a hyperbolic cosine function of time. (orig.)
Chern--Simons theory in the Schroedinger representation
International Nuclear Information System (INIS)
Dunne, G.V.; Jackiw, R.; Trugenberger, C.A.
1989-01-01
We quantize the (2+1)-dimensional Chern--Simons theory in the functional Schroedinger representation. The realization of gauge transformations on states involves a 1-cocycle. We determine this cocycle; we show how solving the Gauss law constraint in the non-Abelian theory requires quantizing the parameter that normalizes the action; we trivialize the 1-cocycle with a spatially non-local cochain related to a 2-dimensional fermion determinant and we find the physical states that satisfy the Gauss law constraint. The quantum holonomy of physical states involves a contribution that is missed when the constraint is solved before quantization. We compute this quantity for the Abelian theory in Minkowski space, where it exhibits an interesting group theoretic structure. (In a note added in proof the corresponding non-Abelian computation is presented.) Also we consider coupling to external sources and offer yet another derivation of the anomalous statistics and spin of the charge and flux carrying particles---a calculation which is especially simple in the functional Schroedinger representation. copyright 1989 Academic Press, Inc
Existence of local degrees of freedom for higher dimensional pure Chern-Simons theories
International Nuclear Information System (INIS)
Banados, M.; Garay, L.J.; Henneaux, M.
1996-01-01
The canonical structure of higher dimensional pure Chern-Simons theories is analyzed. It is shown that these theories have generically a nonvanishing number of local degrees of freedom, even though they are obtained by means of a topological construction. This number of local degrees of freedom is computed as a function of the spacetime dimension and the dimension of the gauge group. copyright 1996 The American Physical Society
Perturbed Chern-Simons theory, fractional statistics, and Yang-Baxter algebra
International Nuclear Information System (INIS)
Chatterjee, A.; Sreedhar, V.V.
1992-01-01
Topological Chern-Simons theory coupled to matter fields is analysed in the framework of Dirac's method of quantising constrained systems in a general class of linear, non-local gauges. We show that in the weak coupling limit gauge invariant operators in the theory transform under an exchange according to a higher dimensional representation of the braid group which is built out of the fundamental representation matrices of the gauge group and thus behave like anyons. We also discover new solutions of the Yang-Baxter equation which emerges as a consistency condition on the structure functions of the operator algebra of the matter fields. (orig.)
On the phase of Chern-Simons theory with complex gauge group
Energy Technology Data Exchange (ETDEWEB)
Gibbs, R.; Mokhtari, S. [Dept. of Phys., Louisiana Tech. Univ., Ruston, LA (United States)
1995-10-07
We compute the eta function for Chern-Simons quantum field theory with complex gauge group. The calculation is performed using the Schwinger expansion technique. We discuss, in particular, the role of the metric on the field configuration space, and demonstrate that for a certain class of acceptable metrics the one-loop phase contribution to the effective action can be calculated explicitly. The result is found to be proportional to a gauge invariant part of the action. (author)
Observables, skein relations, and tetrahedra in Chern-Simons gauge theory
International Nuclear Information System (INIS)
Martin, S.P.
1990-01-01
The observables in three-dimensional Chern-Simons gauge theory are Wilson lines and Wilson graphs. Skein relations are non-trivial identities between expectation values of distinct Wilson graphs. We discuss various kinds of skein relations and the relationships between them. By comparing different kinds of skein relations, we show how to calculate the expectation value of a general tetrahedral Wilson graph. This is shown to be the last and most difficult step in a systematic procedure for calculating the expectation values of arbitrary Wilson graphs in arbitrary representations of arbitrary gauge groups. (orig.)
N = 4 Superconformal Chern-Simons theories with hyper and twisted hyper multiplets
International Nuclear Information System (INIS)
Hosomichi, Kazuo; Lee, Ki-Myeong; Lee, Sungjay; Lee, Sangmin; Park, Jaemo
2008-01-01
We extend the N = 4 superconformal Chern-Simons theories of Gaiotto and Witten to those with additional twisted hyper-multiplets. The new theories are generically linear quiver gauge theories with the two types of hyper-multiplets alternating between gauge groups. Our construction includes the Bagger-Lambert model of SO(4) gauge group. A family of abelian theories are identified with those proposed earlier in the context of the M-crystal model for M2-branes probing (C 2 /Z n ) 2 orbifolds. Possible extension with non-abelian BF couplings and string/M-theory realization are briefly discussed.
Superfiled formulation of Chern-Simons supersymmetry
International Nuclear Information System (INIS)
Birmingham, D.; Rakowski, M.
1989-03-01
We discuss an extra supersymmetry present in the covariantly quantized Chern-Simons action within the superfield formalism. By introducing scalar superfields we show how the component transformations are naturally reproduced from the superfield transformation. When the superspace is extended to include an additional odd coordinate for the BRST symmetry, the entire theory is described by a single odd scalar superfield. The implications of this supersymmetry for the renormalized theory are also discussed. (author). 9 refs
Gauge fixing of Chern-Simons N-extended supergravity
Energy Technology Data Exchange (ETDEWEB)
Ney, W G [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Centro Federal de Educacao Tecnologica (CEFET), Campos dos Goytacazes, RJ (Brazil); Piguet, O [Universidade Federal do Espirito Santo (UFES), ES 29000-001, Vitoria (Brazil); Spalenza, W [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)
2004-08-01
We treat N-extended supergravity in 2+1 space-time dimensions as a Yang-Mills gauge field with Chern-Simons action associated to the N-extended Poincare supergroup. We fix the gauge of this theory within the Batalin-Vilkovisky scheme. (orig.)
Gauge fixing of Chern-Simons N-extended supergravity
International Nuclear Information System (INIS)
Ney, W.G.; Piguet, O.; Spalenza, W.
2004-01-01
We treat N-extended supergravity in 2+1 space-time dimensions as a Yang-Mills gauge field with Chern-Simons action associated to the N-extended Poincare supergroup. We fix the gauge of this theory within the Batalin-Vilkovisky scheme. (orig.)
Remarks on Chern-Simons Invariants
Cattaneo, Alberto S.; Mnëv, Pavel
2010-02-01
The perturbative Chern-Simons theory is studied in a finite-dimensional version or assuming that the propagator satisfies certain properties (as is the case, e.g., with the propagator defined by Axelrod and Singer). It turns out that the effective BV action is a function on cohomology (with shifted degrees) that solves the quantum master equation and is defined modulo certain canonical transformations that can be characterized completely. Out of it one obtains invariants.
Chern-Simons expectation values and quantum horizons from loop quantum gravity and the Duflo map.
Sahlmann, Hanno; Thiemann, Thomas
2012-03-16
We report on a new approach to the calculation of Chern-Simons theory expectation values, using the mathematical underpinnings of loop quantum gravity, as well as the Duflo map, a quantization map for functions on Lie algebras. These new developments can be used in the quantum theory for certain types of black hole horizons, and they may offer new insights for loop quantum gravity, Chern-Simons theory and the theory of quantum groups.
Chern-Simons topological Lagrangians in odd dimensions and their Kaluza-Klein reduction
International Nuclear Information System (INIS)
Wu, Y.
1984-01-01
Clarifying the behavior of generic Chern-Simons secondary invariants under infinitesimal variation and finite gauge transformation, it is proved that they are eligible to be a candidate term in the Lagrangian in odd dimensions (2k-1 for gauge theories and 4k-1 for gravity). The coefficients in front of these terms may be quantized because of topological reasons. As a possible application, the dimensional reduction of such actions in Kaluza-Klein theory is discussed. The difficulty in defining the Chern-Simons action for topologically nontrivial field configurations is pointed out and resolved
Framing and localization in Chern-Simons theories with matter
Energy Technology Data Exchange (ETDEWEB)
Bianchi, Marco S. [Center for Research in String Theory - School of Physics and Astronomy,Queen Mary University of London,Mile End Road, London E1 4NS (United Kingdom); Griguolo, Luca [Dipartimento di Fisica e Scienze della Terra, Università di Parma andINFN Gruppo Collegato di Parma,Viale G.P. Usberti 7/A, 43100 Parma (Italy); Leoni, Matias [Physics Department, FCEyN-UBA & IFIBA-CONICET,Ciudad Universitaria, Pabellón I, 1428, Buenos Aires (Argentina); Mauri, Andrea [Dipartimento di Fisica, Università degli studi di Milano-Bicocca,Piazza della Scienza 3, I-20126 Milano (Italy); Penati, Silvia [Dipartimento di Fisica, Università degli studi di Milano-Bicocca,Piazza della Scienza 3, I-20126 Milano (Italy); INFN, Sezione di Milano-Bicocca,Piazza della Scienza 3, I-20126 Milano (Italy); Seminara, Domenico [Dipartimento di Fisica, Università di Firenze and INFN Sezione di Firenze,via G. Sansone 1, 50019 Sesto Fiorentino (Italy)
2016-06-22
Supersymmetric localization provides exact results that should match QFT computations in some regularization scheme. The agreement is particularly subtle in three dimensions where complex answers from localization procedure sometimes arise. We investigate this problem by studying the expectation value of the 1/6 BPS Wilson loop in planar ABJ(M) theory at three loops in perturbation theory. We reproduce the corresponding term in the localization result and argue that it originates entirely from a non-trivial framing of the circular contour. Contrary to pure Chern-Simons theory, we point out that for ABJ(M) the framing phase is a non-trivial function of the couplings and that it potentially receives contributions from vertex-like diagrams. Finally, we briefly discuss the intimate link between the exact framing factor and the Bremsstrahlung function of the 1/2-BPS cusp.
Equivalence of several Chern-Simons matter models
International Nuclear Information System (INIS)
Chen, W.; Itoi, C.
1994-01-01
Chern-Simons (CS) coupling characterizes not only statistics, but also spin and scaling dimension of matter fields. We demonstrate spin transmutation in relativistic CS matter theory, and moreover show equivalence of several models. We study the CS vector model in some detail, which provides a consistent check to the assertion of the equivalence
Scattering amplitude and bosonization duality in general Chern-Simons vector models
Yokoyama, Shuichi
2016-09-01
We present the exact large N calculus of four point functions in general Chern-Simons bosonic and fermionic vector models. Applying the LSZ formula to the four point function we determine the two body scattering amplitudes in these theories taking a special care for a non-analytic term to achieve unitarity in the singlet channel. We show that the S-matrix enjoys the bosonization duality, an unusual crossing relation and a non-relativistic reduction to Aharonov-Bohm scattering. We also argue that the S-matrix develops a pole in a certain range of coupling constants, which disappears in the range where the theory reduces to the Chern-Simons theory interacting with free fermions.
''Topological'' (Chern-Simons) quantum mechanics
International Nuclear Information System (INIS)
Dunne, G.V.; Jackiw, R.; Trugenberger, C.A.
1990-01-01
We construct quantum-mechanical models that are analogs of three-dimensional, topologically massive as well as Chern-Simons gauge-field theories, and we study the phase-space reductive limiting procedure that takes the former to the latter. The zero-point spectra of operators behave discontinuously in the limit, as a consequence of a nonperturbative quantum-mechanical anomaly. The nature of the limit for wave functions depends on the representation, but is always such that normalization is preserved
International Nuclear Information System (INIS)
Giavarini, G.; Martin, C.P.; Ruiz Ruiz, F.
1993-01-01
We show that the renormalized vacuum expectation value of the Wilson loop for topologically massive abelian gauge theory in bbfR 3 can be defined so that its large-mass limit be the renormalized vaccum expectation value of the Wilson loop for abelian Chern-Simons theory also in bbfR 3 . (orig.)
Chern-Simons theory with vector fermion matter
International Nuclear Information System (INIS)
Giombi, Simone; Minwalla, Shiraz; Prakash, Shiroman; Trivedi, Sandip P.; Wadia, Spenta R.; Yin, Xi
2012-01-01
We study three-dimensional conformal field theories described by U(N) Chern-Simons theory at level k coupled to massless fermions in the fundamental representation. By solving a Schwinger-Dyson equation in light-cone gauge, we compute the exact planar free energy of the theory at finite temperature on R 2 as a function of the 't Hooft coupling λ=N/k. Employing a dimensional reduction regularization scheme, we find that the free energy vanishes at vertical stroke λvertical stroke =1; the conformal theory does not exist for vertical stroke λvertical stroke >1. We analyze the operator spectrum via the anomalous conservation relation for higher spin currents, and in particular show that the higher spin currents do not develop anomalous dimensions at leading order in 1/N. We present an integral equation whose solution in principle determines all correlators of these currents at leading order in 1/N and present explicit perturbative results for all three-point functions up to two loops. We also discuss a light-cone Hamiltonian formulation of this theory where a W ∞ algebra arises. The maximally supersymmetric version of our theory is ABJ model with one gauge group taken to be U(1), demonstrating that a pure higher spin gauge theory arises as a limit of string theory. (orig.)
Effective actions for gauge theories with Chern-Simons terms - I
International Nuclear Information System (INIS)
Bambah, B.A.; Mukku, C.
1989-01-01
The effective Lagrangian for a three-dimensional gauge theory with a Chern-Simons term is evaluated upto one-loop effects. It is shown to be completely finite. It also does not exhibit any imaginary part. The calculation is carried out in a background field analogue of the Feynman gauge and gauge invariance is maintained throughout the calculation. In an appendix an argument is presented as to why this Feynman gauge may be a 'good' gauge for our results to be applied to high temperature QCD and in particular to the quark-gluon plasma. (author). 12 refs
Periodic electromagnetic vacuum in the two-dimensional Yang-Mills theory with the Chern-Simons mass
International Nuclear Information System (INIS)
Skalozub, V.V.; Vilensky, S.A.; Zaslavsky, A.Yu.
1993-06-01
The periodic vacuum structure formed from magnetic and electric fields is derived in the two-dimensional Yang-Mills theory with the Chern-Simons term. It is shown that both the magnetic flux quantization in the fundamental sell and conductivity quantization inherent to the vacuum. Hence, the quantum Hall effect gets its natural explanation. (author). 10 refs
Maxwell-Chern-Simons theory for curved spacetime backgrounds
International Nuclear Information System (INIS)
Kant, E.; Klinkhamer, F.R.
2005-01-01
We consider a modified version of four-dimensional electrodynamics, which has a photonic Chern-Simons-like term with spacelike background vector in the action. Light propagation in curved spacetime backgrounds is discussed using the geometrical-optics approximation. The corresponding light path is modified, which allows for new effects. In a Schwarzschild background, for example, there now exist stable bounded orbits of light rays and the two polarization modes of light rays in unbounded orbits can have different gravitational redshifts
The Origin of Chern-Simons Modified Gravity from an 11 + 3-Dimensional Manifold
Directory of Open Access Journals (Sweden)
J. A. Helayël-Neto
2017-01-01
Full Text Available It is our aim to show that the Chern-Simons terms of modified gravity can be understood as generated by the addition of a 3-dimensional algebraic manifold to an initial 11-dimensional space-time manifold; this builds up an 11+3-dimensional space-time. In this system, firstly, some fields living in the bulk join the fields that live on the 11-dimensional manifold, so that the rank of the gauge fields exceeds the dimension of the algebra; consequently, there emerges an anomaly. To solve this problem, another 11-dimensional manifold is included in the 11+3-dimensional space-time, and it interacts with the initial manifold by exchanging Chern-Simon fields. This mechanism is able to remove the anomaly. Chern-Simons terms actually produce an extra manifold in the pair of 11-dimensional manifolds of the 11+3-space-time. Summing up the topology of both the 11-dimensional manifolds and the topology of the exchanged Chern-Simons manifold in the bulk, we conclude that the total topology shrinks to one, which is in agreement with the main idea of the Big Bang theory.
Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
Hadasz, Leszek; Lindström, Ulf; Roček, Martin; von Unge, Rikard
2004-05-01
We study one- and two-soliton solutions of noncommutative Chern-Simons theory coupled to a nonrelativistic or a relativistic scalar field. In the nonrelativistic case, we find a tower of new stationary time-dependent solutions, all with the same charge density, but with increasing energies. The dynamics of these solitons cannot be studied using traditional moduli space techniques, but we do find a nontrivial symplectic form on the phase space indicating that the moduli space is not flat. In the relativistic case we find the metric on the two soliton moduli space.
Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
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Hadasz, Leszek; Lindstroem, Ulf; Rocek, Martin; Unge, Rikard von
2004-01-01
We study one- and two-soliton solutions of noncommutative Chern-Simons theory coupled to a nonrelativistic or a relativistic scalar field. In the nonrelativistic case, we find a tower of new stationary time-dependent solutions, all with the same charge density, but with increasing energies. The dynamics of these solitons cannot be studied using traditional moduli space techniques, but we do find a nontrivial symplectic form on the phase space indicating that the moduli space is not flat. In the relativistic case we find the metric on the two soliton moduli space
Qiang, Li-E.; Xu, Peng
2015-08-01
Having great accuracy in the range and range rate measurements, the GRACE mission and the planed GRACE follow on mission can in principle be employed to place strong constraints on certain relativistic gravitational theories. In this paper, we work out the range observable of the non-dynamical Chern-Simons modified gravity for the satellite-to-satellite tracking (SST) measurements. We find out that a characteristic time accumulating range signal appears in non-dynamical Chern-Simons gravity, which has no analogue found in the standard parity-preserving metric theories of gravity. The magnitude of this Chern-Simons range signal will reach a few times of cm for each free flight of these SST missions, here is the dimensionless post-Newtonian parameter of the non-dynamical Chern-Simons theory. Therefore, with the 12 years data of the GRACE mission, one expects that the mass scale of the non-dynamical Chern-Simons gravity could be constrained to be larger than eV. For the GRACE FO mission that scheduled to be launched in 2017, the much stronger bound that eV is expected.
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Van de Wetering, J.F.W.H.
1992-01-01
Using perturbative Chern-Simons theory in the almost axial gauge on the euclidean manifold S 1 xR 2 , we give a prescription for the computation of knot invariants. The method gives the correct expectation value of the unknot to all orders in perturbation theory and gives the correct answer for the spectral-parameter-dependent universal R-matrix to second order. All results are derived for a general semi-simple Lie algebra. (orig.)
Classical optics in generalized Maxwell Chern-Simons theory
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Burgess, M.; Leinaas, J.M.; Loevvik, O.M.
1993-03-01
The authors consider the propagation of electromagnetic waves in a two-dimensional polarizable medium endowed with Chern-Simons terms. The dispersion relation (refractive index) of the waves is computed and the existence of linear birefringence and anomalous dispersion is shown. When absorption is taken into account, the classic signature of a Voigt effect is found. In the case where linearly-polarized, three-dimensional waves pass through a two-dimensional plane, it is shown that there is optical activity, and the analogue of Verdet's constant is computed. 19 refs., 2 figs
Papapetrou energy-momentum tensor for Chern-Simons modified gravity
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Guarrera, David; Hariton, A. J.
2007-01-01
We construct a conserved, symmetric energy-momentum (pseudo-)tensor for Chern-Simons modified gravity, thus demonstrating that the theory is Lorentz invariant. The tensor is discussed in relation to other gravitational energy-momentum tensors and analyzed for the Schwarzschild, Reissner-Nordstrom, and Friedmann-Robertson-Walker solutions. To our knowledge this is the first confirmation that the Reissner-Nordstrom and Friedmann-Robertson-Walker metrics are solutions of the modified theory
Light-front dynamics of Chern-Simons systems
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Srivastava, P.P.
1994-10-01
The Chern-Simons theory coupled to complex scalars is quantized on the light-front in the local light-cone gauge by constructing the self-consistent Hamiltonian theory. It is shown that no inconsistency arises on using two local gauge-fixing conditions in the Dirac procedure. The light-front Hamiltonian turns out to be simple and the framework may be useful to construct renormalized field theory of particles with fractional statistics (anyons). The theory is shown to be relativistic and the extra term in the transformation of the matter field under space rotations, interpreted in previous works as anomaly, is argued to be gauge artefact. (author). 20 refs
What we think about the higher dimensional Chern-Simons theories
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Fock, V.V.; Nekrasov, N.A.; Rosly, A.A.; Selivanov, K.G.
1992-01-01
This paper reports that one of the most interesting developments in mathematical physics was the investigation of the so-called topological field theories i.e. such theories which do not need a metric on the manifold for their definition a d hence the observable of which are topologically invariant. The Chern-Simons (CS) functionals considered as actions give us examples the theories of such a type. The CS theory on a 3d manifold was firstly considered in the Abelian case by A.S. Schwartz and then after papers of E. Witten there has been an explosive process of publications on this subject. This paper discusses topological invariants of the manifolds (like the Ray-Singer torsion) computed by the quantum field theory methods; conformal blocks of 2d conformal field theories as vectors in the CS theory Hilbert space; correlators of Wilson loop and the invariants of 1d links in 3d manifolds; braid groups; unusual relations between spin and statistics; here we would like to consider the generalization of a part of the outlined ideas to the CS theories on higher dimensional manifolds. Some of our results intersect with
Chern-Simons gravity in four dimensions
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Morales, Ivan; Neves, Bruno; Piguet, Olivier; Oporto, Zui
2017-01-01
Five-dimensional Chern-Simons theory with (anti-)de Sitter SO(1,5) or SO(2,4) gauge invariance presents an alternative to general relativity with cosmological constant. We consider the zero modes of its Kaluza-Klein compactification to four dimensions. Solutions with vanishing torsion are obtained in the cases of a spherically symmetric 3-space and of a homogeneous and isotropic 3-space, which reproduce the Schwarzshild-de Sitter and ΛCDM cosmological solutions of general relativity. We also check that vanishing torsion is a stable feature of the solutions. (orig.)
Chern-Simons gravity in four dimensions
Energy Technology Data Exchange (ETDEWEB)
Morales, Ivan; Neves, Bruno; Piguet, Olivier [Universidade Federal de Vicosa (UFV), Departamento de Fisica, Vicosa, MG (Brazil); Oporto, Zui [Universidade Federal de Vicosa (UFV), Departamento de Fisica, Vicosa, MG (Brazil); Universidad Mayor de San Andres, Carrera de Fisica, La Paz (Bolivia, Plurinational State of)
2017-02-15
Five-dimensional Chern-Simons theory with (anti-)de Sitter SO(1,5) or SO(2,4) gauge invariance presents an alternative to general relativity with cosmological constant. We consider the zero modes of its Kaluza-Klein compactification to four dimensions. Solutions with vanishing torsion are obtained in the cases of a spherically symmetric 3-space and of a homogeneous and isotropic 3-space, which reproduce the Schwarzshild-de Sitter and ΛCDM cosmological solutions of general relativity. We also check that vanishing torsion is a stable feature of the solutions. (orig.)
Superconformal Chern-Simons theories and AdS4/CFT3 correspondence
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Benna, Marcus; Klebanov, Igor; Klose, Thomas; Smedbaeck, Mikael
2008-01-01
We discuss the N = 2 superspace formulation of the N = 8 superconformal Bagger-Lambert-Gustavsson theory, and of the N = 6 superconformal Aharony-Bergman-Jafferis-Maldacena U(N) x U(N) Chern-Simons theory. In particular, we prove the full SU(4) R-symmetry of the ABJM theory. We then consider orbifold projections of this theory that give non-chiral and chiral (U(N) x U(N)) n superconformal quiver gauge theories. We argue that these theories are dual to certain AdS 4 x S 7 /(Z n x Z k -tilde) backgrounds of M-theory. We also study a SU(3) invariant mass term in the superpotential that makes the N = 8 theory flow to a N = 2 superconformal gauge theory with a sextic superpotential. We conjecture that this gauge theory is dual to the U(1) R x SU(3) invariant extremum of the N = 8 gauged supergravity, which was discovered by N. Warner 25 years ago and whose uplifting to 11 dimensions was found more recently.
Holography in Lovelock Chern-Simons AdS gravity
Cvetković, Branislav; Miskovic, Olivera; Simić, Dejan
2017-08-01
We analyze holographic field theory dual to Lovelock Chern-Simons anti-de Sitter (AdS) gravity in higher dimensions using first order formalism. We first find asymptotic symmetries in the AdS sector showing that they consist of local translations, local Lorentz rotations, dilatations and non-Abelian gauge transformations. Then, we compute 1-point functions of energy-momentum and spin currents in a dual conformal field theory and write Ward identities. We find that the holographic theory possesses Weyl anomaly and also breaks non-Abelian gauge symmetry at the quantum level.
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Rey, Soo-Jong; Suyama, Takao; Yamaguchi, Satoshi
2009-01-01
We study Wilson loop operators in three-dimensional, N = 6 superconformal Chern-Simons theory dual to IIA superstring theory on AdS 4 x CP 3 . Novelty of Wilson loop operators in this theory is that, for a given contour, there are two linear combinations of Wilson loop transforming oppositely under time-reversal transformation. We show that one combination is holographically dual to IIA fundamental string, while orthogonal combination is set to zero. We gather supporting evidences from detailed comparative study of generalized time-reversal transformations in both D2-brane worldvolume and ABJM theories. We then classify supersymmetric Wilson loops and find at most 1/6 supersymmetry. We next study Wilson loop expectation value in planar perturbation theory. For circular Wilson loop, we find features remarkably parallel to circular Wilson loop in N = 4 super Yang-Mills theory in four dimensions. First, all odd loop diagrams vanish identically and even loops contribute nontrivial contributions. Second, quantum corrected gauge and scalar propagators take the same form as those of N = 4 super Yang-Mills theory. Combining these results, we propose that expectation value of circular Wilson loop is given by Wilson loop expectation value in pure Chern-Simons theory times zero-dimensional Gaussian matrix model whose variance is specified by an interpolating function of 't Hooft coupling. We suggest the function interpolates smoothly between weak and strong coupling regime, offering new test ground of the AdS/CFT correspondence.
Large N non-perturbative effects in N=4 superconformal Chern-Simons theories
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Hatsuda, Yasuyuki; Honda, Masazumi; Okuyama, Kazumi
2015-07-01
We investigate the large N instanton effects of partition functions in a class of N = 4 circular quiver Chern-Simons theories on a three-sphere. Our analysis is based on the supersymmetry localization and the Fermi-gas formalism. The resulting matrix model can be regarded as a two-parameter deformation of the ABJM matrix model, and has richer non-perturbative structures. Based on a systematic semi-classical analysis, we find analytic expressions of membrane instanton corrections. We also exactly compute the partition function for various cases and find some exact forms of worldsheet instanton corrections, which appear as quantum mechanical non-perturbative corrections in the Fermi-gas system.
On the quantization of the coefficient of the abelian Chern-Simons term
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Polychronakos, A.P.
1990-01-01
We point out that the coefficient of the abelian Chern-Simons term need not be quantized, even in the case of compact U(1) group. Instead, the quantum theory is qualitatively different for integer or rotational values of that coefficient. (orig.)
Non-minimal Maxwell-Chern-Simons theory and the composite Fermion model
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Paschoal, Ricardo C.; Helayel Neto, Jose A.
2003-01-01
The magnetic field redefinition in Jain's composite fermion model for the fractional quantum Hall effect is shown to be effective described by a mean-field approximation of a model containing a Maxwell-Chern-Simons gauge field nominally coupled to matter. Also an explicit non-relativistic limit of the non-minimal (2+1) D Dirac's equation is derived. (author)
Entropy for gravitational Chern-Simons terms by squashed cone method
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Guo, Wu-Zhong; Miao, Rong-Xin
2016-01-01
In this paper we investigate the entropy of gravitational Chern-Simons terms for the horizon with non-vanishing extrinsic curvatures, or the holographic entanglement entropy for arbitrary entangling surface. In 3D there is no anomaly of entropy. But the original squashed cone method can not be used directly to get the correct result. For higher dimensions the anomaly of entropy would appear, still, we can not use the squashed cone method directly. That is becasuse the Chern-Simons action is not gauge invariant. To get a reasonable result we suggest two methods. One is by adding a boundary term to recover the gauge invariance. This boundary term can be derived from the variation of the Chern-Simons action. The other one is by using the Chern-Simons relation dΩ_4_n_−_1=tr(R"2"n). We notice that the entropy of tr(R"2"n) is a total derivative locally, i.e. S=ds_C_S. We propose to identify s_C_S with the entropy of gravitational Chern-Simons terms Ω_4_n_−_1. In the first method we could get the correct result for Wald entropy in arbitrary dimension. In the second approach, in addition to Wald entropy, we can also obtain the anomaly of entropy with non-zero extrinsic curvatures. Our results imply that the entropy of a topological invariant, such as the Pontryagin term tr(R"2"n) and the Euler density, is a topological invariant on the entangling surface.
N=1,2 supergravities in 2+1 dimensions as Chern-Simons theories
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Li Miao.
1988-12-01
In this letter we report the results on the explanation of the Lagrangians of 2+1 supergravities as graded Chern-Simons terms, which are derived from inspiration of Witten's recent work on exact solvability of 2+1 Einstein gravity. Further implications will be considered elsewhere. (author). 8 refs
Boundary effects in 2 + 1 dimensional Maxwell-Chern-Simons theory
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Ferrer, E.J.; Incera, V. de la.
1996-09-01
The boundary effects in the screening of an applied magnetic field in a finite temperature 2 + 1 dimensional model of charged fermions minimally coupled to Maxwell and Chern-Simons fields are investigated. It is found that in a sample with only one boundary -a half-plane- a total Meissner effect takes place, while in a sample with two boundaries -an infinite strip- the external magnetic field partially penetrates the material. (author). 17 refs
Finite-size effect of the dyonic giant magnons in N=6 super Chern-Simons theory
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Ahn, Changrim; Bozhilov, P.
2009-01-01
We consider finite-size effects for the dyonic giant magnon of the type IIA string theory on AdS 4 xCP 3 by applying the Luescher μ-term formula which is derived from a recently proposed S matrix for the N=6 super Chern-Simons theory. We compute explicitly the effect for the case of a symmetric configuration where the two external bound states, each of A and B particles, have the same momentum p and spin J 2 . We compare this with the classical string theory result which we computed by reducing it to the Neumann-Rosochatius system. The two results match perfectly.
Topics in Two-Dimensional Quantum Gravity and Chern-Simons Gauge Theories
Zemba, Guillermo Raul
A series of studies in two and three dimensional theories is presented. The two dimensional problems are considered in the framework of String Theory. The first one determines the region of integration in the space of inequivalent tori of a tadpole diagram in Closed String Field Theory, using the naive Witten three-string vertex. It is shown that every surface is counted an infinite number of times and the source of this behavior is identified. The second study analyzes the behavior of the discrete matrix model of two dimensional gravity without matter using a mathematically well-defined construction, confirming several conjectures and partial results from the literature. The studies in three dimensions are based on Chern Simons pure gauge theory. The first one deals with the projection of the theory onto a two-dimensional surface of constant time, whereas the second analyzes the large N behavior of the SU(N) theory and makes evident a duality symmetry between the only two parameters of the theory. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253 -1690.).
Nontopological bare solutions in the relativistic self-dual Maxwell-Chern-Simons-Higgs model
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Han, Jongmin; Jang, Jaeduk
2005-01-01
In this paper we prove the existence of the radially symmetric nontopological bare solutions in the relativistic self-dual Maxwell-Chern-Simons-Higgs model. We also verify the Chern-Simons limit for those solutions
Integrable spin chain in superconformal Chern-Simons theory
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Bak, Dongsu; Rey, Soo-Jong
2008-01-01
N = 6 superconformal Chern-Simons theory was proposed as gauge theory dual to Type IIA string theory on AdS 4 x CP 3 . We study integrability of the theory from conformal dimension spectrum of single trace operators at planar limit. At strong 't Hooft coupling, the spectrum is obtained from excitation energy of free superstring on OSp(6|4; R)/SO(3, 1) x SU(3) x U(1) supercoset. We recall that the worldsheet theory is integrable classically by utilizing well-known results concerning sigma model on symmetric space. With R-symmetry group SU(4), we also solve relevant Yang-Baxter equation for a spin chain system associated with the single trace operators. From the solution, we construct alternating spin chain Hamiltonian involving three-site interactions between 4 and 4-bar . At weak 't Hooft coupling, we study gauge theory perturbatively, and calculate action of dilatation operator to single trace operators up to two loops. To ensure consistency, we computed all relevant Feynman diagrams contributing to the dilatation opeator. We find that resulting spin chain Hamiltonian matches with the Hamiltonian derived from Yang-Baxter equation. We further study new issues arising from the shortest gauge invariant operators TrY I Y † J = (15, 1). We observe that 'wrapping interactions' are present, compute the true spectrum and find that the spectrum agrees with prediction from supersymmetry. We also find that scaling dimension computed naively from alternating spin chain Hamiltonian coincides with the true spectrum. We solve Bethe ansatz equations for small number of excitations, and find indications of correlation between excitations of 4's and 4-bar 's and of nonexistence of mesonic (44-bar ) bound-state.
Chern-Simons, Wess-Zumino and other cocycles from Kashiwara-Vergne and associators
Alekseev, Anton; Naef, Florian; Xu, Xiaomeng; Zhu, Chenchang
2018-03-01
Descent equations play an important role in the theory of characteristic classes and find applications in theoretical physics, e.g., in the Chern-Simons field theory and in the theory of anomalies. The second Chern class (the first Pontrjagin class) is defined as p= where F is the curvature 2-form and is an invariant scalar product on the corresponding Lie algebra g. The descent for p gives rise to an element ω =ω _3+ω _2+ω _1+ω _0 of mixed degree. The 3-form part ω _3 is the Chern-Simons form. The 2-form part ω _2 is known as the Wess-Zumino action in physics. The 1-form component ω _1 is related to the canonical central extension of the loop group LG. In this paper, we give a new interpretation of the low degree components ω _1 and ω _0. Our main tool is the universal differential calculus on free Lie algebras due to Kontsevich. We establish a correspondence between solutions of the first Kashiwara-Vergne equation in Lie theory and universal solutions of the descent equation for the second Chern class p. In more detail, we define a 1-cocycle C which maps automorphisms of the free Lie algebra to one forms. A solution of the Kashiwara-Vergne equation F is mapped to ω _1=C(F). Furthermore, the component ω _0 is related to the associator Φ corresponding to F. It is surprising that while F and Φ satisfy the highly nonlinear twist and pentagon equations, the elements ω _1 and ω _0 solve the linear descent equation.
Induced Chern-Simons term in lattice QCD at finite temperature
International Nuclear Information System (INIS)
Borisenko, O.A.; Petrov, V.K.; Zinovjev, G.M.
1995-01-01
The general conditions for the Chern-Simons action to be induced as a non-universal contribution of fermionic determinant are formulated in finite-temperature lattice QCD. The dependence of the corresponding coefficient in the action on non-universal parameters (chemical potentials, vacuum features, etc.) is explored. Special attention is paid to the role of A 0 -condensate if it is available in this theory. ((orig.))
Chern-Simons theory and atypical Hall conductivity in the Varma phase
Menezes, Natália; Smith, Cristiane Morais; Palumbo, Giandomenico
2018-02-01
In this article, we analyze the topological response of a fermionic model defined on the Lieb lattice in the presence of an electromagnetic field. The tight-binding model is built in terms of three species of spinless fermions and supports a topological Varma phase due to the spontaneous breaking of time-reversal symmetry. In the low-energy regime, the emergent effective Hamiltonian coincides with the so-called Duffin-Kemmer-Petiau (DKP) Hamiltonian, which describes relativistic pseudospin-0 quasiparticles. By considering a minimal coupling between the DKP quasiparticles and an external Abelian gauge field, we first find the Landau-level spectrum by fixing the Landau gauge; then we compute the emergent Chern-Simons theory for a weak-electromagnetic-field regime. The corresponding Hall conductivity reveals an atypical quantum Hall effect, which can be simulated in an artificial Lieb lattice.
From Lorentz-Chern-Simons to Massive Gravity in 2+1 dimensions
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Pino, Simón del [Instituto de Física, Facultad de Ciencias, Pontificia Universidad Católica de Valparaíso,Av. Universidad 330, Curauma, Valparaíso (Chile); Giribet, Gaston [Physique Théorique et Mathématique, Université Libre de Bruxelles andInternational Solvay Institutes,Campus Plaine C.P. 231, Bruxelles, B-1050 (Belgium); Departamento de Física, Universidad de Buenos Aires and IFIBA-CONICET,Ciudad Universitaria, Pabellón I, Buenos Aires, 1428 (Argentina); Instituto de Física, Facultad de Ciencias, Pontificia Universidad Católica de Valparaíso,Av. Universidad 330, Curauma, Valparaíso (Chile); Toloza, Adolfo [Instituto de Física, Facultad de Ciencias, Pontificia Universidad Católica de Valparaíso,Av. Universidad 330, Curauma, Valparaíso (Chile); Centro de Estudios Científicos CECs,Arturo Prat 514, Valdivia (Chile); Zanelli, Jorge [Centro de Estudios Científicos CECs,Arturo Prat 514, Valdivia (Chile)
2015-06-17
We propose a generalization of Chiral Gravity, which follows from considering a Chern-Simons action for the spin connection with anti-symmetric contorsion. The theory corresponds to Topologically Massive Gravity at the chiral point non-minimally coupled to an additional scalar mode that gathers the torsion degree of freedom. In this setup, the effective cosmological constant (the inverse of the curvature radius of maximally symmetric solutions) is either negative or zero, and it enters as an integration constant associated to the value of the contorsion at infinity. We explain how this is not in conflict with the Zamolodchikov’s c-theorem holding in the dual boundary theory. In fact, we conjecture that the theory formulated about three-dimensional Anti-de Sitter space is dual to a two-dimensional conformal field theory whose right- and left-moving central charges are given by c{sub R}=24k and c{sub L}=0, respectively, being k the level of the Chern-Simons action. We study the classical theory both at the linear and non-linear level. In particular, we show how Chiral Gravity is included as a special sector. In addition, the theory has other sectors, which we explore; we exhibit analytic exact solutions that are not solutions of Topologically Massive Gravity (and, consequently, neither of General Relativity) and still satisfy Brown-Henneaux asymptotically AdS{sub 3} boundary conditions.
Solitons and bubbles in models with Chern-Simons term
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Masperi, L.
1992-07-01
It is shown that a gauge theory for complex scalar field with up to sextic self-interactions and a Chern-Simons term in 2 + 1 dimensions has solitons which may become bubbles of the stable broken-symmetry phase in a medium of the symmetric one producing the first-order phase transition. In the non-relativistic limit scale invariance prevents the determination of an optimal bubble size. Possible extensions to 3 + 1 dimensions of bubbles of string type are indicated. (author). 8 refs
Maxwell-Chern-Simons Casimir effect. II. Circular boundary conditions
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Milton, K.A.; Ng, Y.J.
1992-01-01
In odd-dimensional spaces, gauge invariance permits a Chern-Simons mass term for the gauge fields in addition to the usual Maxwell-Yang-Mills kinetic energy term. We study the Casimir effect in such a (2+1)-dimensional Abelian theory. The case of parallel conducting lines was considered by us in a previous paper. Here we discuss the Casimir effect for a circle and examine the effect of finite temperature. The Casimir stress is found to be attractive at both low and high temperatures
Confinement in Maxwell-Chern-Simons planar quantum electrodynamics and the 1/N approximation
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Hofmann, Christoph P.; Raya, Alfredo; Madrigal, Saul Sanchez
2010-01-01
We study the analytical structure of the fermion propagator in planar quantum electrodynamics coupled to a Chern-Simons term within a four-component spinor formalism. The dynamical generation of parity-preserving and parity-violating fermion mass terms is considered, through the solution of the corresponding Schwinger-Dyson equation for the fermion propagator at leading order of the 1/N approximation in Landau gauge. The theory undergoes a first-order phase transition toward chiral symmetry restoration when the Chern-Simons coefficient θ reaches a critical value which depends upon the number of fermion families considered. Parity-violating masses, however, are generated for arbitrarily large values of the said coefficient. On the confinement scenario, complete charge screening - characteristic of the 1/N approximation - is observed in the entire (N,θ)-plane through the local and global properties of the vector part of the fermion propagator.
Anyonic states in Chern-Simons theory
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Haller, K.; Lim-Lombridas, E.
1994-01-01
We discuss the canonical quantization of Chern-Simons theory in 2+1 dimensions, minimally coupled to a Dirac spinor field, first in the temporal gauge and then in the Coulomb gauge. In our temporal gauge formulation, Gauss's law and the gauge condition A 0 =0 are implemented by embedding the formulation in an appropriate physical subspace. We construct a Fock space of charged particle states that satisfy Gauss's law, and show that they obey fermion, not fractional statistics. The gauge-invariant spinor field that creates these charged states from the vacuum obeys the anticommutation rules that generally apply to spinor fields. The Hamiltonian, when described in the representation in which the charged fermions are the propagating particle excitations that obey Gauss's law, contains an interaction between charge and transverse current densities. We observe that the implementation of Gauss's law and the gauge condition does not require us to use fields with graded commutator algebras or particle excitations with fractional statistics. In our Coulomb gauge formulation, we implement Gauss's law and the gauge condition ∂ l A l =0 by the Dirac-Bergmann procedure. In this formulation, the constrained gauge fields become functionals of the spinor fields, and are not independent degrees of freedom. The formulation in the Coulomb gauge confirms the results we obtained in the temporal gauge: The ''Dirac-Bergmann'' anticommutation rule for the charged spinor fiels ψ and ψ degree that have both been constrained to obey Gauss's law is precisely identical to the canonical spinor anticommutation rule that generates standard fermion statistics. And we also show that the Hamiltonians for charged particle states in our temporal and Coulomb gauge formulations are identical, once Gauss's law has been implemented in both cases
Chern-Simons field theory of two-dimensional electrons in the lowest Landau level
International Nuclear Information System (INIS)
Zhang, L.
1996-01-01
We propose a fermion Chern-Simons field theory describing two-dimensional electrons in the lowest Landau level. This theory is constructed with a complete set of states, and the lowest-Landau-level constraint is enforced through a δ functional described by an auxiliary field λ. Unlike the field theory constructed directly with the states in the lowest Landau level, this theory allows one, utilizing the physical picture of open-quote open-quote composite fermion,close-quote close-quote to study the fractional quantum Hall states by mapping them onto certain integer quantum Hall states; but, unlike its application in the unconstrained theory, such a mapping is sensible only when interactions between electrons are present. An open-quote open-quote effective mass,close-quote close-quote which characterizes the scale of low energy excitations in the fractional quantum Hall systems, emerges naturally from our theory. We study a Gaussian effective theory and interpret physically the dressed stationary point equation for λ as an equation for the open-quote open-quote mass renormalization close-quote close-quote of composite fermions. copyright 1996 The American Physical Society
η-INVARIANT AND CHERN-SIMONS CURRENT
Institute of Scientific and Technical Information of China (English)
ZHANG WEIPING
2005-01-01
The author presents an alternate proof of the Bismut-Zhang localization formula of ηinvariants, when the target manifold is a sphere, by using ideas of mod k index theory instead of the difficult analytic localization techniques of Bismut-Lebeau. As a consequence, it is shown that the R/Z part of the aualytically defined η invariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a higher dimensional sphere. As a preliminary application, the author discusses the relation with the Atiyah-Patodi-Singer R/Z index theorem for unitary flat vector bundles,and proves an R refinement in the case where the Dirac operator is replaced by the Signature operator.
Null geodesics and shadow of a rotating black hole in extended Chern-Simons modified gravity
International Nuclear Information System (INIS)
Amarilla, Leonardo; Eiroa, Ernesto F.; Giribet, Gaston
2010-01-01
The Chern-Simons modification to general relativity in four dimensions consists of adding to the Einstein-Hilbert term a scalar field that couples to the first-class Pontryagin density. In this theory, which has attracted considerable attention recently, the Schwarzschild metric persists as an exact solution, and this is why this model resists several observational constraints. In contrast, the spinning black hole solution of the theory is not given by the Kerr metric but by a modification of it, so far only known for slow rotation and small coupling constant. In the present paper, we show that, in this approximation, the null geodesic equation can be integrated, and this allows us to investigate the shadow cast by a black hole. We discuss how, in addition to the angular momentum of the solution, the coupling to the Chern-Simons term deforms the shape of the shadow.
International Nuclear Information System (INIS)
Park, Mu-In
2008-01-01
Recently, the Banados-Teitelboim-Zanelli (BTZ) black hole in the presence of the gravitational Chern-Simons term has been studied, and it is found that the usual thermodynamic quantities, like the black hole mass, angular momentum, and entropy, are modified. But, for large values of the gravitational Chern-Simons coupling where the modification terms dominate the original terms some exotic behaviors occur, like the roles of the mass and angular momentum are interchanged and the entropy depends more on the inner horizon area than the outer one. A basic physical problem of this system is that the form of entropy does not guarantee the second law of thermodynamics, in contrast to the Bekenstein-Hawking entropy. Moreover, this entropy does not agree with the statistical entropy, in contrast to a good agreement for small values of the gravitational Chern-Simons coupling. Here I find that there is another entropy formula where the usual Bekenstein-Hawking form dominates the inner-horizon term again, as in the small gravitational Chern-Simons coupling case, such that the second law of thermodynamics can be guaranteed. I also find that the new entropy formula agrees with the statistical entropy based on the holographic anomalies for the whole range of the gravitational Chern-Simons coupling. This reproduces, in the limit of a vanishing Einstein-Hilbert term, the recent result about the exotic BTZ black holes, where their masses and angular momenta are completely interchanged and the entropies depend only on the area of the inner horizon. I compare the result of the holographic approach with the classical-symmetry-algebra-based approach, and I find exact agreements even with the higher-derivative corrections of the gravitational Chern-Simons term. This provides a nontrivial check of the AdS/CFT correspondence, in the presence of higher-derivative terms in the gravity action
Gravitational waves from quasicircular black-hole binaries in dynamical Chern-Simons gravity.
Yagi, Kent; Yunes, Nicolás; Tanaka, Takahiro
2012-12-21
Dynamical Chern-Simons gravity cannot be strongly constrained with current experiments because it reduces to general relativity in the weak-field limit. This theory, however, introduces modifications in the nonlinear, dynamical regime, and thus it could be greatly constrained with gravitational waves from the late inspiral of black-hole binaries. We complete the first self-consistent calculation of such gravitational waves in this theory. For favorable spin orientations, advanced ground-based detectors may improve existing solar system constraints by 6 orders of magnitude.
All Chern-Simons invariants of 4D, N=1 gauged superform hierarchies
Energy Technology Data Exchange (ETDEWEB)
Becker, Katrin; Becker, Melanie; III, William D. Linch [George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University,College Station, TX 77843-4242 (United States); Randall, Stephen [Department of Physics, University of California,Berkeley, CA 94720-7300 (United States); Robbins, Daniel [Department of Physics, University at Albany,Albany, NY 12222 (United States)
2017-04-19
We give a geometric description of supersymmetric gravity/(non-)abelian p-form hierarchies in superspaces with 4D, N=1 super-Poincaré invariance. These hierarchies give rise to Chern-Simons-like invariants, such as those of the 5D, N=1 graviphoton and the eleven-dimensional 3-form but also generalizations such as Green-Schwarz-like/BF-type couplings. Previous constructions based on prepotential superfields are reinterpreted in terms of p-forms in superspace thereby elucidating the underlying geometry. This vastly simplifies the calculations of superspace field-strengths, Bianchi identities, and Chern-Simons invariants. Using this, we prove the validity of a recursive formula for the conditions defining these actions for any such tensor hierarchy. Solving it at quadratic and cubic orders, we recover the known results for the BF-type and cubic Chern-Simons actions. As an application, we compute the quartic invariant ∼AdAdAdA+… relevant, for example, to seven-dimensional supergravity compactifications.
N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
International Nuclear Information System (INIS)
Aharony, Ofer; Bergman, Oren; Maldacena, Juan; Jafferis, Daniel Louis
2008-01-01
We construct three dimensional Chern-Simons-matter theories with gauge groups U(N) x U(N) and SU(N) x SU(N) which have explicit N = 6 superconformal symmetry. Using brane constructions we argue that the U(N) x U(N) theory at level k describes the low energy limit of N M2-branes probing a C 4 /Z k singularity. At large N the theory is then dual to M-theory on AdS 4 x S 7 /Z k . The theory also has a 't Hooft limit (of large N with a fixed ratio N/k) which is dual to type IIA string theory on AdS 4 x CP 3 . For k = 1 the theory is conjectured to describe N M2-branes in flat space, although our construction realizes explicitly only six of the eight supersymmetries. We give some evidence for this conjecture, which is similar to the evidence for mirror symmetry in d = 3 gauge theories. When the gauge group is SU(2) x SU(2) our theory has extra symmetries and becomes identical to the Bagger-Lambert theory.
Electron-electron attractive interaction in Maxwell-Chern-Simons QED3 at zero temperature
International Nuclear Information System (INIS)
Belich, H.; Ferreira Junior, M.M.; Helayel-Neto, J.A.; Ferreira Junior, M.M.
2001-04-01
One discusses the issue of low-energy electron-electron bound states in the Maxwell-Chern-Simons model coupled to QED 3 with spontaneous breaking of a local U(1)-symmetry. The scattering potential, in the non-relativistic limit, steaming from the electron-electron Moeller scattering, mediated by the Maxwell-Chern-Simons-Proca gauge field and the Higgs scalar, might be attractive by fine-tuning properly the physical parameters of the model. (author)
Fermion zero modes in the vortex background of a Chern-Simons-Higgs theory with a hidden sector
Energy Technology Data Exchange (ETDEWEB)
Lozano, Gustavo [Departamento de Física, FCEYN Universidad de Buenos Aires & IFIBA CONICET,Pabellón 1 Ciudad Universitaria, 1428 Buenos Aires (Argentina); Mohammadi, Azadeh [Departamento de Física, Universidade Federal da Paraíba,58.059-970, Caixa Postal 5.008, João Pessoa, PB (Brazil); Schaposnik, Fidel A. [Departamento de Física, Universidad Nacional de La Plata/IFLP/CICBA,CC 67, 1900 La Plata (Argentina)
2015-11-06
In this paper we study a 2+1 dimensional system in which fermions are coupled to the self-dual topological vortex in U(1)×U(1) Chern-Simons theory, where both U(1) gauge symmetries are spontaneously broken. We consider two Abelian Higgs scalars with visible and hidden sectors coupled to a fermionic field through three interaction Lagrangians, where one of them violates the fermion number. Using a fine tuning procedure, we could obtain the number of the fermionic zero modes which is equal to the absolute value of the sum of the vortex numbers in the visible and hidden sectors.
First law of black ring thermodynamics in higher dimensional Chern-Simons gravity
International Nuclear Information System (INIS)
Rogatko, Marek
2007-01-01
The physical process version and the equilibrium state version of the first law of black ring thermodynamics in n-dimensional Einstein gravity with Chern-Simons term were derived. This theory constitutes the simplest generalization of the five-dimensional one admitting a stationary black ring solution. The equilibrium state version of the first law of black ring mechanics was achieved by choosing any cross section of the event horizon to the future of the bifurcation surface
Chern-Simons action for inhomogeneous Virasoro group as extension of three dimensional flat gravity
Energy Technology Data Exchange (ETDEWEB)
Barnich, Glenn [Physique Théorique et Mathématique, Université Libre de Bruxelles and International Solvay Institutes, Campus Plaine C.P. 231, B-1050 Bruxelles (Belgium); Giribet, Gastón [Physique Théorique et Mathématique, Université Libre de Bruxelles and International Solvay Institutes, Campus Plaine C.P. 231, B-1050 Bruxelles (Belgium); Universidad de Buenos Aires FCEN-UBA and IFIBA-CONICET, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires (Argentina); Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Leston, Mauricio [Instituto de Astronomía y Física del Espacio IAFE-CONICET, Ciudad Universitaria, Pabellón IAFE, C.C. 67 Suc. 28, 1428 Buenos Aires (Argentina)
2015-07-15
We initiate the study of a Chern-Simons action associated to the semi-direct sum of the Virasoro algebra with its coadjoint representation. This model extends the standard Chern-Simons formulation of three dimensional flat gravity and is similar to the higher-spin extension of three dimensional anti-de Sitter or flat gravity. The extension can also be constructed for the exotic but not for the cosmological constant deformation of flat gravity.
Electron-electron attractive interaction in Maxwell-Chern-Simons QED{sub 3} at zero temperature
Energy Technology Data Exchange (ETDEWEB)
Belich, H.; Ferreira Junior, M.M.; Helayel-Neto, J.A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). E-mail: belich@cbpf.br; manojr@cbpf.br; helayel@gft.ucp.br; Ferreira Junior, M.M. [Universidade Catolica de Petropolis, RJ (Brazil). Grupo de Fisica Teorica. E-mail: delcima@gft.ucp.br
2001-04-01
One discusses the issue of low-energy electron-electron bound states in the Maxwell-Chern-Simons model coupled to QED{sub 3} with spontaneous breaking of a local U(1)-symmetry. The scattering potential, in the non-relativistic limit, steaming from the electron-electron Moeller scattering, mediated by the Maxwell-Chern-Simons-Proca gauge field and the Higgs scalar, might be attractive by fine-tuning properly the physical parameters of the model. (author)
Multi-boundary entanglement in Chern-Simons theory and link invariants
Energy Technology Data Exchange (ETDEWEB)
Balasubramanian, Vijay [David Rittenhouse Laboratory, University of Pennsylvania,209 S.33rd Street, Philadelphia, PA 19104 (United States); Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB) andInternational Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium); Fliss, Jackson R.; Leigh, Robert G. [Department of Physics, University of Illinois,1110 W. Green Street, Urbana, IL 61801 (United States); Parrikar, Onkar [David Rittenhouse Laboratory, University of Pennsylvania,209 S.33rd Street, Philadelphia, PA 19104 (United States)
2017-04-11
We consider Chern-Simons theory for gauge group G at level k on 3-manifolds M{sub n} with boundary consisting of n topologically linked tori. The Euclidean path integral on M{sub n} defines a quantum state on the boundary, in the n-fold tensor product of the torus Hilbert space. We focus on the case where M{sub n} is the link-complement of some n-component link inside the three-sphere S{sup 3}. The entanglement entropies of the resulting states define framing-independent link invariants which are sensitive to the topology of the chosen link. For the Abelian theory at level k (G=U(1){sub k}) we give a general formula for the entanglement entropy associated to an arbitrary (m|n−m) partition of a generic n-component link into sub-links. The formula involves the number of solutions to certain Diophantine equations with coefficients related to the Gauss linking numbers (mod k) between the two sublinks. This formula connects simple concepts in quantum information theory, knot theory, and number theory, and shows that entanglement entropy between sublinks vanishes if and only if they have zero Gauss linking (mod k). For G=SU(2){sub k}, we study various two and three component links. We show that the 2-component Hopf link is maximally entangled, and hence analogous to a Bell pair, and that the Whitehead link, which has zero Gauss linking, nevertheless has entanglement entropy. Finally, we show that the Borromean rings have a “W-like' entanglement structure (i.e., tracing out one torus does not lead to a separable state), and give examples of other 3-component links which have “GHZ-like” entanglement (i.e., tracing out one torus does lead to a separable state).
Anyons, spin, and statistics in (2+1)-dimensional U(1)-scalar Chern-Simons gauge field theory
International Nuclear Information System (INIS)
Graziano, E.; Rothe, K.D.
1994-01-01
We present a detailed analysis of the quantum field theory of a Chern-Simons field coupled minimally to massive charged bosonic matter. This analysis is carried out in the Coulomb and covariant gauges. Some aspects concerning the transformation law of the fields under Poincare transformations are clarified. Emphasis is placed on gauge-invariant operators. The order and disorder operators are constructed from their dual algebra. The order operator is shown to obey anyonic statistics. The correlator of the disorder operator is computed in the large boson-mass limit, and the corresponding cluster properties are discussed. In the absence of a symmetry-breaking Higgs potential, there is no evidence for the ground state being anyonic
Lie-algebra expansions, Chern-Simons theories and the Einstein-Hilbert Lagrangian
International Nuclear Information System (INIS)
Edelstein, Jose D.; Hassaine, Mokhtar; Troncoso, Ricardo; Zanelli, Jorge
2006-01-01
Starting from gravity as a Chern-Simons action for the AdS algebra in five dimensions, it is possible to modify the theory through an expansion of the Lie algebra that leads to a system consisting of the Einstein-Hilbert action plus non-minimally coupled matter. The modified system is gauge invariant under the Poincare group enlarged by an Abelian ideal. Although the resulting action naively looks like general relativity plus corrections due to matter sources, it is shown that the non-minimal couplings produce a radical departure from GR. Indeed, the dynamics is not continuously connected to the one obtained from Einstein-Hilbert action. In a matter-free configuration and in the torsionless sector, the field equations are too strong a restriction on the geometry as the metric must satisfy both the Einstein and pure Gauss-Bonnet equations. In particular, the five-dimensional Schwarzschild geometry fails to be a solution; however, configurations corresponding to a brane-world with positive cosmological constant on the worldsheet are admissible when one of the matter fields is switched on. These results can be extended to higher odd dimensions
Vortex dynamics in self-dual Chern-Simons-Higgs systems
International Nuclear Information System (INIS)
Kim, Y.; Lee, K.
1994-01-01
We consider vortex dynamics in self-dual Chern-Simons-Higgs systems. We show that the naive Aharonov-Bohm phase is the inverse of the statistical phase expected from the vortex spin, and that the self-dual configurations of vortices are degenerate in energy but not in angular momentum. We also use the path integral formalism to derive the dual formulation of Chern-Simons-Higgs systems in which vortices appear as charged particles. We argue that in addition to the electromagnetic interaction, there is an additional interaction between vortices, the so-called Magnus force, and that these forces can be put together into a single ''dual electromagnetic'' interaction. This dual electromagnetic interaction leads to the right statistical phase. We also derive and study the effective action for slowly moving vortices, which contains terms both linear and quadratic in the vortex velocity. We show that vortices can be bounded to each other by the Magnus force
Holography in three-dimensional Kerr-de Sitter space with a gravitational Chern-Simons term
International Nuclear Information System (INIS)
Park, Mu-In
2008-01-01
The holographic description of the three-dimensional Kerr-de Sitter space with a gravitational Chern-Simons term is studied, in the context of dS/CFT correspondence. The space has only one (cosmological) event horizon and its mass and angular momentum are identified from the holographic energy-momentum tensor at the asymptotic infinity. The thermodynamic entropy of the cosmological horizon is computed directly from the first law of thermodynamics, with the conventional Hawking temperature, and it is found that the usual Gibbons-Hawking entropy is modified. It is remarked that, due to the gravitational Chern-Simons term, (a) the results go beyond the analytic continuation from AdS, (b) the maximum-mass/N-bound conjecture may be violated and (c) the three-dimensional cosmology is chiral. A statistical mechanical computation of the entropy, from a Cardy-like formula for a dual CFT at the asymptotic boundary, is discussed. Some remarks on the technical differences in the Chern-Simons energy-momentum tensor, from the literature, are also made
Surface theorem for the Chern-Simons axion coupling
DEFF Research Database (Denmark)
Olsen, Thomas; Taherinejad, Maryam; Vanderbilt, David
2017-01-01
The Chern-Simons axion coupling of a bulk insulator is only defined modulo a quantum of e2/h. The quantized part of the coupling is uniquely defined for a bounded insulating sample, but it depends on the specific surface termination.Working in a slab geometry and representing the valence bands...... in terms of hybridWannier functions, we show how to determine that quantized part from the excess Chern number of the hybridWannier sheets located near the surface of the slab. The procedure is illustrated for a tight-binding model consisting of coupled quantum anomalous Hall layers. By slowly modulating...... the model parameters it is possible to transfer one unit of Chern number from the bottom to the top surface over the course of a cyclic evolution of the bulk Hamiltonian, changing the surface anomalous Hall conductivity by a quantum of conductance e2/h. When the evolution of the surface Hamiltonian is also...
Chern-Simons forms and four-dimensional N=1 superspace geometry
International Nuclear Information System (INIS)
Girardi, G.; Grimm, R.
1986-12-01
The complete superspace geometry for Yang-Mills, chiral U(1) and Lorentz Chern-Simons forms is constructed. The analysis is completely off-shell and covers the cases of minimal, new minimal and 16-16 supergravity. Supersymmetry is guaranteed by construction. Invariant superfield actions are proposed
Hydrodynamic electron flow in a Weyl semimetal slab: Role of Chern-Simons terms
Gorbar, E. V.; Miransky, V. A.; Shovkovy, I. A.; Sukhachov, P. O.
2018-05-01
The hydrodynamic flow of the chiral electron fluid in a Weyl semimetal slab of finite thickness is studied by using the consistent hydrodynamic theory. The latter includes viscous, anomalous, and vortical effects, as well as accounts for dynamical electromagnetism. The energy and momentum separations between the Weyl nodes are taken into account via the topological Chern-Simons contributions in the electric current and charge densities in Maxwell's equations. When an external electric field is applied parallel to the slab, it is found that the electron fluid velocity has a nonuniform profile determined by the viscosity and the no-slip boundary conditions. Most remarkably, the fluid velocity field develops a nonzero component across the slab that gradually dissipates when approaching the surfaces. This abnormal component of the flow arises due to the anomalous Hall voltage induced by the topological Chern-Simons current. Another signature feature of the hydrodynamics in Weyl semimetals is a strong modification of the anomalous Hall current along the slab in the direction perpendicular to the applied electric field. Additionally, it is found that the topological current induces an electric potential difference between the surfaces of the slab that is strongly affected by the hydrodynamic flow.
International Nuclear Information System (INIS)
Teh, R.
1989-07-01
Vortex-like and string-like solutions of 2+1 Dim. SU(2) YM theory with the Chern-Simons term are discussed. Two ansatze are constructed which yield respectively analytic Bessel function solutions and elliptic function solutions. The Bessel function solutions are vortex-like and tend to the same vacuum state as the Ginzburg-Landau vortex solution at large ρ. The Jacobi elliptic function solutions are string-like, have finite energy and magnetic flux concentrated along a line in the x 1 - x 2 plane. (author). 18 refs
Initial value formulation of dynamical Chern-Simons gravity
Delsate, Térence; Hilditch, David; Witek, Helvi
2015-01-01
We derive an initial value formulation for dynamical Chern-Simons gravity, a modification of general relativity involving parity-violating higher derivative terms. We investigate the structure of the resulting system of partial differential equations thinking about linearization around arbitrary backgrounds. This type of consideration is necessary if we are to establish well-posedness of the Cauchy problem. Treating the field equations as an effective field theory we find that weak necessary conditions for hyperbolicity are satisfied. For the full field equations we find that there are states from which subsequent evolution is not determined. Generically the evolution system closes, but is not hyperbolic in any sense that requires a first order pseudodifferential reduction. In a cursory mode analysis we find that the equations of motion contain terms that may cause ill-posedness of the initial value problem.
Dense Chern-Simons matter with fermions at large N
Energy Technology Data Exchange (ETDEWEB)
Geracie, Michael; Goykhman, Mikhail; Son, Dam T. [Kadanoff Center for Theoretical Physics, Enrico Fermi Institute and Department of Physics,The University of Chicago, 5620 S. Ellis Av., Chicago, IL, 60637 (United States)
2016-04-18
In this paper we investigate properties of Chern-Simons theory coupled to massive fermions in the large N limit. We demonstrate that at low temperatures the system is in a Fermi liquid state whose features can be systematically compared to the standard phenomenological theory of Landau Fermi liquids. This includes matching microscopically derived Landau parameters with thermodynamic predictions of Landau Fermi liquid theory. We also calculate the exact conductivity and viscosity tensors at zero temperature and finite chemical potential. In particular we point out that the Hall conductivity of an interacting system is not entirely accounted for by the Berry flux through the Fermi sphere. Furthermore, investigation of the thermodynamics in the non-relativistic limit reveals novel phenomena at strong coupling. As the ’t Hooft coupling λ approaches 1, the system exhibits an extended intermediate temperature regime in which the thermodynamics is described by neither the quantum Fermi liquid theory nor the classical ideal gas law. Instead, it can be interpreted as a weakly coupled quantum Bose gas.
Dense Chern-Simons matter with fermions at large N
International Nuclear Information System (INIS)
Geracie, Michael; Goykhman, Mikhail; Son, Dam T.
2016-01-01
In this paper we investigate properties of Chern-Simons theory coupled to massive fermions in the large N limit. We demonstrate that at low temperatures the system is in a Fermi liquid state whose features can be systematically compared to the standard phenomenological theory of Landau Fermi liquids. This includes matching microscopically derived Landau parameters with thermodynamic predictions of Landau Fermi liquid theory. We also calculate the exact conductivity and viscosity tensors at zero temperature and finite chemical potential. In particular we point out that the Hall conductivity of an interacting system is not entirely accounted for by the Berry flux through the Fermi sphere. Furthermore, investigation of the thermodynamics in the non-relativistic limit reveals novel phenomena at strong coupling. As the ’t Hooft coupling λ approaches 1, the system exhibits an extended intermediate temperature regime in which the thermodynamics is described by neither the quantum Fermi liquid theory nor the classical ideal gas law. Instead, it can be interpreted as a weakly coupled quantum Bose gas.
Dense Chern-Simons matter with fermions at large N
Geracie, Michael; Goykhman, Mikhail; Son, Dam T.
2016-04-01
In this paper we investigate properties of Chern-Simons theory coupled to massive fermions in the large N limit. We demonstrate that at low temperatures the system is in a Fermi liquid state whose features can be systematically compared to the standard phenomenological theory of Landau Fermi liquids. This includes matching microscopically derived Landau parameters with thermodynamic predictions of Landau Fermi liquid theory. We also calculate the exact conductivity and viscosity tensors at zero temperature and finite chemical potential. In particular we point out that the Hall conductivity of an interacting system is not entirely accounted for by the Berry flux through the Fermi sphere. Furthermore, investigation of the thermodynamics in the non-relativistic limit reveals novel phenomena at strong coupling. As the 't Hooft coupling λ approaches 1, the system exhibits an extended intermediate temperature regime in which the thermodynamics is described by neither the quantum Fermi liquid theory nor the classical ideal gas law. Instead, it can be interpreted as a weakly coupled quantum Bose gas.
Large N Chern-Simons with massive fundamental fermions — A model with no bound states
International Nuclear Information System (INIS)
Frishman, Yitzhak; Sonnenschein, Jacob
2014-01-01
In a previous paper http://dx.doi.org/10.1007/JHEP12(2013)091, we analyzed the theory of massive fermions in the fundamental representation coupled to a U(N) Chern-Simons gauge theory in three dimensions at level K. It was done in the large N, large K limits where λ=(N/K) was kept fixed. Among other results, we showed there that there are no high mass “quark anti-quark" bound states. Here we show that there are no bound states at all.
Dimensional reduction of a Lorentz and CPT-violating Maxwell-Chern-Simons model
International Nuclear Information System (INIS)
Belich, H. Jr.; Helayel Neto, J.A.; Ferreira, M.M. Jr.; Maranhao Univ., Sao Luiz, MA; Orlando, M.T.D.; Espirito Santo Univ., Vitoria, ES
2003-01-01
Taking as starting point a Lorentz and CPT non-invariant Chern-Simons-like model defined in 1+3 dimensions, we proceed realizing its dimensional to D = 1+2. One then obtains a new planar model, composed by the Maxwell-Chern-Simons (MCS) sector, a Klein-Gordon massless scalar field, and a coupling term that mixes the gauge field to the external vector, ν μ . In spite of breaking Lorentz invariance in the particle frame, this model may preserve the CPT symmetry for a single particular choice of ν μ . Analyzing the dispersion relations, one verifies that the reduced model exhibits stability, but the causality can be jeopardized by some modes. The unitary of the gauge sector is assured without any restriction , while the scalar sector is unitary only in the space-like case. (author)
Bound states in the (2+1)D scalar electrodynamics with Chern-Simons term
International Nuclear Information System (INIS)
Gomes, M.O.C.; Malacarne, L.C.
1994-01-01
This work studies the existence of bound states for the 3-dimensions scalar electrodynamics, with the Chern-Simons. Quantum field theory is used for calculation of the M fi scattering matrices, in the non-relativistic approximation. The field propagators responsible for the interaction in the scattering processes have been calculated, and scattering matrices have been constructed. After obtaining the scattering matrix, the cross section in the quantum field theory has been compared with the quantum mechanic cross section in the Born approximation, allowing to obtain the form of the potential responsible for the interactions in the scattering processes. The possibility of bound states are analyzed by using the Schroedinger equation
BPS-kink and more global solutions of the Chern-Simons (super)gravity term
International Nuclear Information System (INIS)
Grumiller, D.
2004-01-01
We study the supersymmetry of the Kaluza-Klein reduced gravitational Chern-Simons term in two dimensions and propose supergravity transformations that allow for some supersymmetry of the kink solution. (author)
Electric Chern-Simons term, enlarged exotic Galilei symmetry and noncommutative plane
International Nuclear Information System (INIS)
Olmo, Mariano A. del; Plyushchay, Mikhail S.
2006-01-01
The extended exotic planar model for a charged particle is constructed. It includes a Chern-Simons-like term for a dynamical electric field, but produces usual equations of motion for the particle in background constant uniform electric and magnetic fields. The electric Chern-Simons term is responsible for the noncommutativity of the boost generators in the 10-dimensional enlarged exotic Galilei symmetry algebra of the extended system. The model admits two reduction schemes by the integrals of motion, one of which reproduces the usual formulation for the charged particle in external constant electric and magnetic fields with associated field-deformed Galilei symmetry, whose commuting boost generators are identified with the nonlocal in time Noether charges reduced on-shell. Another reduction scheme, in which electric field transmutes into the commuting space translation generators, extracts from the model a free particle on the noncommutative plane described by the twofold centrally extended Galilei group of the nonrelativistic anyons
Dimensional reduction of a Lorentz and CPT-violating Maxwell-Chern-Simons model
Energy Technology Data Exchange (ETDEWEB)
Belich, H. Jr.; Helayel Neto, J.A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Teoria de Campos e Particulas; Grupo de Fisica Teorica Jose Leite Lopes, Petropolis, RJ (Brazil); E-mails: belich@cbpf.br; helayel@cbpf.br; Ferreira, M.M. Jr. [Grupo de Fisica Teorica Jose Leite Lopes, Petropolis, RJ (Brazil); Maranhao Univ., Sao Luiz, MA (Brazil). Dept. de Fisica]. E-mail: manojr@cbpf.br; Orlando, M.T.D. [Grupo de Fisica Teorica Jose Leite Lopes, Petropolis, RJ (Brazil); Espirito Santo Univ., Vitoria, ES (Brazil). Dept. de Fisica e Quimica; E-mail: orlando@cce.ufes.br
2003-01-01
Taking as starting point a Lorentz and CPT non-invariant Chern-Simons-like model defined in 1+3 dimensions, we proceed realizing its dimensional to D = 1+2. One then obtains a new planar model, composed by the Maxwell-Chern-Simons (MCS) sector, a Klein-Gordon massless scalar field, and a coupling term that mixes the gauge field to the external vector, {nu}{sup {mu}}. In spite of breaking Lorentz invariance in the particle frame, this model may preserve the CPT symmetry for a single particular choice of {nu}{sup {mu}} . Analyzing the dispersion relations, one verifies that the reduced model exhibits stability, but the causality can be jeopardized by some modes. The unitary of the gauge sector is assured without any restriction , while the scalar sector is unitary only in the space-like case. (author)
Asymptotic conformal invariance in a non-Abelian Chern-Simons-matter model
Energy Technology Data Exchange (ETDEWEB)
Acebal, J.L. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Campos e Particulas]. E-mail: acebal@cbpf.br
2002-08-01
One shows here the existence of solutions to the Callan-Symanzik equation for the non-Abelian SU(2) Chern-Simons-matter model which exhibits asymptotic conformal invariance to every order in perturbative theory. The conformal symmetry in the classical domain is shown to hold by means of a local criteria based on the trace of the energy-momentum tensor. By using recently exhibited regimes for the dependence between the several couplings in which the set of {beta}-functions vanish, the asymptotic conformal invariance of the model appears to be valid in the quantum domain. By considering the SU (n) case the possible non validity of the proof for a particular {eta} would be merely accidental. (author)
Low regularity solutions of the Chern-Simons-Higgs equations in the Lorentz gauge
Directory of Open Access Journals (Sweden)
Nikolaos Bournaveas
2009-09-01
Full Text Available We prove local well-posedness for the 2+1-dimensional Chern-Simons-Higgs equations in the Lorentz gauge with initial data of low regularity. Our result improves earlier results by Huh [10, 11].
Higher derivative extensions of 3d Chern-Simons models: conservation laws and stability
International Nuclear Information System (INIS)
Kaparulin, D.S.; Karataeva, I.Yu.; Lyakhovich, S.L.
2015-01-01
We consider the class of higher derivative 3d vector field models with the field equation operator being a polynomial of the Chern-Simons operator. For the nth-order theory of this type, we provide a general recipe for constructing n-parameter family of conserved second rank tensors. The family includes the canonical energy-momentum tensor, which is unbounded, while there are bounded conserved tensors that provide classical stability of the system for certain combinations of the parameters in the Lagrangian. We also demonstrate the examples of consistent interactions which are compatible with the requirement of stability. (orig.)
Holographic entanglement for Chern-Simons terms
International Nuclear Information System (INIS)
Azeyanagi, Tatsuo; Loganayagam, R.; Ng, Gim Seng
2017-01-01
We derive the holographic entanglement entropy contribution from pure and mixed gravitational Chern-Simons(CS) terms in AdS 2k+1 . This is done through two different methods: first, by a direct evaluation of CS action in a holographic replica geometry and second by a descent of Dong’s derivation applied to the corresponding anomaly polynomial. In lower dimensions (k=1,2), the formula coincides with the Tachikawa formula for black hole entropy from gravitational CS terms. New extrinsic curvature corrections appear for k≥3: we give explicit and concise expressions for the two pure gravitational CS terms in AdS 7 and present various consistency checks, including agreements with the black hole entropy formula when evaluated at the bifurcation surface.
Holographic entanglement for Chern-Simons terms
Energy Technology Data Exchange (ETDEWEB)
Azeyanagi, Tatsuo [Département de Physique, Ecole Normale Supérieure, CNRS,24 rue Lhomond, 75005 Paris (France); Loganayagam, R. [School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Ng, Gim Seng [Department of Physics, McGill University,Montréal, QC H3A 2T8 (Canada)
2017-02-01
We derive the holographic entanglement entropy contribution from pure and mixed gravitational Chern-Simons(CS) terms in AdS{sub 2k+1}. This is done through two different methods: first, by a direct evaluation of CS action in a holographic replica geometry and second by a descent of Dong’s derivation applied to the corresponding anomaly polynomial. In lower dimensions (k=1,2), the formula coincides with the Tachikawa formula for black hole entropy from gravitational CS terms. New extrinsic curvature corrections appear for k≥3: we give explicit and concise expressions for the two pure gravitational CS terms in AdS{sub 7} and present various consistency checks, including agreements with the black hole entropy formula when evaluated at the bifurcation surface.
Holographic entanglement for Chern-Simons terms
Azeyanagi, Tatsuo; Loganayagam, R.; Ng, Gim Seng
2017-02-01
We derive the holographic entanglement entropy contribution from pure and mixed gravitational Chern-Simons(CS) terms in AdS2 k+1. This is done through two different methods: first, by a direct evaluation of CS action in a holographic replica geometry and second by a descent of Dong's derivation applied to the corresponding anomaly polynomial. In lower dimensions ( k = 1 , 2), the formula coincides with the Tachikawa formula for black hole entropy from gravitational CS terms. New extrinsic curvature corrections appear for k ≥ 3: we give explicit and concise expressions for the two pure gravitational CS terms in AdS7 and present various consistency checks, including agreements with the black hole entropy formula when evaluated at the bifurcation surface.
Field redefinitions and Chern-Simons terms in the heterotic string
International Nuclear Information System (INIS)
Bern, Z.; Shimada, T.
1987-07-01
Field redefinitions in the low energy effective action of the heterotic string are discussed. A field redefinition is constructed which generates the local counterterm that transforms the Lorentz into the gravitational form of the anomaly. We also discuss the field redefinition which torsionizes the Lorentz Chern-Simons term and its relation to an amplitude matching study of the compatibility of torsion with the Gauss-Bonnet combination. (orig.)
Multi-cut solutions in Chern-Simons matrix models
Morita, Takeshi; Sugiyama, Kento
2018-04-01
We elaborate the Chern-Simons (CS) matrix models at large N. The saddle point equations of these matrix models have a curious structure which cannot be seen in the ordinary one matrix models. Thanks to this structure, an infinite number of multi-cut solutions exist in the CS matrix models. Particularly we exactly derive the two-cut solutions at finite 't Hooft coupling in the pure CS matrix model. In the ABJM matrix model, we argue that some of multi-cut solutions might be interpreted as a condensation of the D2-brane instantons.
d=3 Chern-Simons action, supergravity and quantization
International Nuclear Information System (INIS)
Dayi, O.F.
1989-01-01
An interpretation of three-dimensional simple supergravity as a pure Chern-Simons gauge action is shown to be valid up to the one loop level. Canonical quantization of this system does not lead to an explicit definition of the physical Hilbert space. Hence another formulation of the N = 1 three-dimensional supergravity is introduced. In this formalism an explicit definition of the physical Hilbert space is possible, but still one has to solve the problems of showing that there exists a global set of coordinates and of defining the inner product. (author). 10 refs
Self-duality in Maxwell-Chern-Simons theories with non minimal coupling with matter field
Chandelier, F; Masson, T; Wallet, J C
2000-01-01
We consider a general class of non-local MCS models whose usual minimal coupling to a conserved current is supplemented with a (non-minimal) magnetic Pauli-type coupling. We find that the considered models exhibit a self-duality whenever the magnetic coupling constant reaches a special value: the partition function is invariant under a set of transformations among the parameter space (the duality transformations) while the original action and its dual counterpart have the same form. The duality transformations have a structure similar to the one underlying self-duality of the (2+1)-dimensional Z sub n - Abelian Higgs model with Chern-Simons and bare mass term.
Deformed N = 8 supergravity from IIA strings and its Chern-Simons duals
Energy Technology Data Exchange (ETDEWEB)
Guarino, Adolfo [Nikhef Theory Group, Amsterdam (Netherlands); Jafferis, Daniel L. [Center for the Fundamental Laws of Nature, Harvard University, Cambridge, MA (United States); Varela, Oscar [Center for the Fundamental Laws of Nature, Harvard University, Cambridge, MA (United States); Centre de Physique Theorique, Ecole Polytechnique, CNRS UMR 7644, Palaiseau (France)
2016-04-15
Do electric/magnetic deformations of N = 8 supergravity enjoy a string/M-theory origin, or are they just a fourdimensional artefact? We address this question for the gauging of a group closely related to SO(8): its contraction ISO(7). We argue that the deformed ISO(7) supergravity arises from consistent truncation of massive IIA supergravity on S{sup 6}, and its electric/magnetic deformation parameter descends directly from the Romans mass. The critical points of the supergravity uplift to AdS{sub 4} massive type IIA vacua and the corresponding CFT{sub 3} duals are identified as super-Chern-Simons-matter theories with gauge group SU(N) and level k given also by the Romans mass. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Exact solution of Chern-Simons-matter matrix models with characteristic/orthogonal polynomials
International Nuclear Information System (INIS)
Tierz, Miguel
2016-01-01
We solve for finite N the matrix model of supersymmetric U(N) Chern-Simons theory coupled to N f fundamental and N f anti-fundamental chiral multiplets of R-charge 1/2 and of mass m, by identifying it with an average of inverse characteristic polynomials in a Stieltjes-Wigert ensemble. This requires the computation of the Cauchy transform of the Stieltjes-Wigert polynomials, which we carry out, finding a relationship with Mordell integrals, and hence with previous analytical results on the matrix model. The semiclassical limit of the model is expressed, for arbitrary N f , in terms of a single Hermite polynomial. This result also holds for more general matter content, involving matrix models with double-sine functions.
Non abelian Chern-Simons topological coupling from self-interaction
International Nuclear Information System (INIS)
Aragone, C.; Stephany, R.J.E.
1986-01-01
It is shown that the self-interaction mechanism drives in one step the topologically coupled-Maxwell-second rank antisymmetric tensor system into the Chern-Simons coupled -non abelian- (second rank) antisymmetric tensor action. Only one step is required to saturate the process because the action for the initial Maxwell-antisymmetric tensor system is given in its first-order form. The self-interaction mechanism works both for the original Chapline-Manton form of the action and for the dual form. (Author) [pt
Chern-Simons induced spin factors in noncovariant gauges
International Nuclear Information System (INIS)
Tanaka, I.
1993-01-01
We study Chern-Simons induced spin factors in noncovariant metric-independent gauges, such as the axial gauge and the Coulomb gauge. These spin factors are defined without loop splitting. We find that they are equal to integers and have particular geometrical meanings. In the axial gauge, this integer is the writhe number of a link diagram defined by the projection of a loop to the time direction. In the Coulomb gauge, it is suggested that this integer is also the writhe number of a link diagram, defined by the projection of a loop to a spatial plane
Flat connections in three-manifolds and classical ChernâSimons invariant
Directory of Open Access Journals (Sweden)
Enore Guadagnini
2017-12-01
Full Text Available A general method for the construction of smooth flat connections on 3-manifolds is introduced. The procedure is strictly connected with the deduction of the fundamental group of a manifold M by means of a Heegaard splitting presentation of M. For any given matrix representation of the fundamental group of M, a corresponding flat connection A on M is specified. It is shown that the associated classical ChernâSimons invariant assumes then a canonical form which is given by the sum of two contributions: the first term is determined by the intersections of the curves in the Heegaard diagram, and the second term is the volume of a region in the representation group which is determined by the representation of Ï1(M and by the Heegaard gluing homeomorphism. Examples of flat connections in topologically nontrivial manifolds are presented and the computations of the associated classical ChernâSimons invariants are illustrated.
Lattice implementation of Abelian gauge theories with Chern-Simons number and an axion field
Figueroa, Daniel G.; Shaposhnikov, Mikhail
2018-01-01
Real time evolution of classical gauge fields is relevant for a number of applications in particle physics and cosmology, ranging from the early Universe to dynamics of quark-gluon plasma. We present an explicit non-compact lattice formulation of the interaction between a shift-symmetric field and some U (1) gauge sector, a (x)FμνF˜μν, reproducing the continuum limit to order O (dxμ2) and obeying the following properties: (i) the system is gauge invariant and (ii) shift symmetry is exact on the lattice. For this end we construct a definition of the topological number density K =FμνF˜μν that admits a lattice total derivative representation K = Δμ+ Kμ, reproducing to order O (dxμ2) the continuum expression K =∂μKμ ∝ E → ṡ B → . If we consider a homogeneous field a (x) = a (t), the system can be mapped into an Abelian gauge theory with Hamiltonian containing a Chern-Simons term for the gauge fields. This allow us to study in an accompanying paper the real time dynamics of fermion number non-conservation (or chirality breaking) in Abelian gauge theories at finite temperature. When a (x) = a (x → , t) is inhomogeneous, the set of lattice equations of motion do not admit however a simple explicit local solution (while preserving an O (dxμ2) accuracy). We discuss an iterative scheme allowing to overcome this difficulty.
Ricci dark energy in Chern-Simons modified gravity
Energy Technology Data Exchange (ETDEWEB)
Silva, J.G.; Santos, A.F. [Universidade Federal de Mato Grosso (UFMT), Campo Grande, MT (Brazil)
2013-07-01
Full text: Currently the accelerated expansion of the universe has been strongly confirmed by some independent experiments such as the Cosmic Microwave Background Radiation (CMBR) and Sloan Digital Sky Survey (SDSS). In an attempt to explain this phenomenon there are two possible paths; first option - propose corrections to general relativity, second option - assuming that there is a dominant component of the universe, a kind of antigravity called dark energy. Any way that we intend to follow, there are numerous models that attempt to explain this effect. One of the models of modified gravity that has stood out in recent years is the Chern-Simons modified gravity. This modification consists in the addition of the Pontryagin density, which displays violation of parity symmetry in Einstein-Hilbert action. From among the various models proposed for dark energy there are some that are based on the holographic principle, known as holographic dark energy. Such models are based on the idea that the energy density of a given system is proportional to the inverse square of some characteristic length of the system. From these studies, here we consider the model proposed by Gao et. al., a model of dark energy where the characteristic length is given by the average radius of the Ricci scalar. Thus, the dark energy density is proportional to the Ricci scalar, i.e., ρ{sub x} ∝ R. It is a phenomenologically viable model and displays results similar to that presented by the cosmological model ACDM. In this work, we have considered the Ricci dark energy model in the dynamic Chern-Simons modified gravity. We show that in this context the evolution of the scale factor is similar to that displayed by the modified Chaplygin gas. (author)
Ricci dark energy in Chern-Simons modified gravity
International Nuclear Information System (INIS)
Silva, J.G.; Santos, A.F.
2013-01-01
Full text: Currently the accelerated expansion of the universe has been strongly confirmed by some independent experiments such as the Cosmic Microwave Background Radiation (CMBR) and Sloan Digital Sky Survey (SDSS). In an attempt to explain this phenomenon there are two possible paths; first option - propose corrections to general relativity, second option - assuming that there is a dominant component of the universe, a kind of antigravity called dark energy. Any way that we intend to follow, there are numerous models that attempt to explain this effect. One of the models of modified gravity that has stood out in recent years is the Chern-Simons modified gravity. This modification consists in the addition of the Pontryagin density, which displays violation of parity symmetry in Einstein-Hilbert action. From among the various models proposed for dark energy there are some that are based on the holographic principle, known as holographic dark energy. Such models are based on the idea that the energy density of a given system is proportional to the inverse square of some characteristic length of the system. From these studies, here we consider the model proposed by Gao et. al., a model of dark energy where the characteristic length is given by the average radius of the Ricci scalar. Thus, the dark energy density is proportional to the Ricci scalar, i.e., ρ x ∝ R. It is a phenomenologically viable model and displays results similar to that presented by the cosmological model ACDM. In this work, we have considered the Ricci dark energy model in the dynamic Chern-Simons modified gravity. We show that in this context the evolution of the scale factor is similar to that displayed by the modified Chaplygin gas. (author)
The Maxwell-Chern-Simons gravity, and its cosmological implications
Energy Technology Data Exchange (ETDEWEB)
Haghani, Zahra; Shahidi, Shahab [Damghan University, School of Physics, Damghan (Iran, Islamic Republic of); Harko, Tiberiu [Babes-Bolyai University, Department of Physics, Cluj-Napoca (Romania); University College London, Department of Mathematics, London (United Kingdom)
2017-08-15
We consider the cosmological implications of a gravitational theory containing two vector fields coupled via a generalized Chern-Simons term. One of the vector fields is the usual Maxwell field, while the other is a constrained vector field with constant norm included in the action via a Lagrange multiplier. The theory admits a de Sitter type solution, with healthy cosmological perturbations. We also show that there are seven degrees of freedom that propagate on top of de Sitter space-time, consisting of two tensor polarizations, four degrees of freedom related to the two vector fields, and a scalar degree of freedom that makes one of the vector fields massive. We investigate the cosmological evolution of Bianchi type I space-time, by assuming that the matter content of the Universe can be described by the stiff and dust. The cosmological evolution of the Bianchi type I Universe strongly depends on the initial conditions of the physical quantities, as well as on the model parameters. The mean anisotropy parameter, and the deceleration parameter, are also studied, and we show that independently of the matter equation of state the cosmological evolution of the Bianchi type I Universe always ends in an isotropic de Sitter type phase. (orig.)
Dirac matrices for Chern-Simons gravity
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Izaurieta, Fernando; Ramirez, Ricardo; Rodriguez, Eduardo [Departamento de Matematica y Fisica Aplicadas, Universidad Catolica de la Santisima Concepcion, Alonso de Ribera 2850, 4090541 Concepcion (Chile)
2012-10-06
A genuine gauge theory for the Poincare, de Sitter or anti-de Sitter algebras can be constructed in (2n- 1)-dimensional spacetime by means of the Chern-Simons form, yielding a gravitational theory that differs from General Relativity but shares many of its properties, such as second order field equations for the metric. The particular form of the Lagrangian is determined by a rank n, symmetric tensor invariant under the relevant algebra. In practice, the calculation of this invariant tensor can be reduced to the computation of the trace of the symmetrized product of n Dirac Gamma matrices {Gamma}{sub ab} in 2n-dimensional spacetime. While straightforward in principle, this calculation can become extremely cumbersome in practice. For large enough n, existing computer algebra packages take an inordinate long time to produce the answer or plainly fail having used up all available memory. In this talk we show that the general formula for the trace of the symmetrized product of 2n Gamma matrices {Gamma}{sub ab} can be written as a certain sum over the integer partitions s of n, with every term being multiplied by a numerical cofficient {alpha}{sub s}. We then give a general algorithm that computes the {alpha}-coefficients as the solution of a linear system of equations generated by evaluating the general formula for different sets of tensors B{sup ab} with random numerical entries. A recurrence relation between different coefficients is shown to hold and is used in a second, 'minimal' algorithm to greatly speed up the computations. Runtime of the minimal algorithm stays below 1 min on a typical desktop computer for up to n = 25, which easily covers all foreseeable applications of the trace formula.
Static solutions in Einstein-Chern-Simons gravity
Energy Technology Data Exchange (ETDEWEB)
Crisóstomo, J.; Gomez, F.; Mella, P.; Quinzacara, C.; Salgado, P., E-mail: jcrisostomo@udec.cl, E-mail: fernagomez@udec.cl, E-mail: patriciomella@udec.cl, E-mail: cristian.cortesq@uss.cl, E-mail: pasalgad@udec.cl [Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile)
2016-06-01
In this paper we study static solutions with more general symmetries than the spherical symmetry of the five-dimensional Einstein-Chern-Simons gravity. In this context, we study the coupling of the extra bosonic field h{sup a} with ordinary matter which is quantified by the introduction of an energy-momentum tensor field associated with h{sup a}. It is found that exist (i) a negative tangential pressure zone around low-mass distributions (μ < μ{sub 1}) when the coupling constant α is greater than zero; (ii) a maximum in the tangential pressure, which can be observed in the outer region of a field distribution that satisfies μ < μ{sub 2}; (iii) solutions that behave like those obtained from models with negative cosmological constant. In such a situation, the field h{sup a} plays the role of a cosmological constant.
Poisson structure and symmetry in the Chern-Simons formulation of (2 + 1)-dimensional gravity
International Nuclear Information System (INIS)
Meusburger, C; Schroers, B J
2003-01-01
In the formulation of (2 + 1)-dimensional gravity as a Chern-Simons gauge theory, the phase space is the moduli space of flat Poincare group connections. Using the combinatorial approach developed by Fock and Rosly, we give an explicit description of the phase space and its Poisson structure for the general case of a genus g oriented surface with punctures representing particles and a boundary playing the role of spatial infinity. We give a physical interpretation and explain how the degrees of freedom associated with each handle and each particle can be decoupled. The symmetry group of the theory combines an action of the mapping class group with asymptotic Poincare transformations in a nontrivial fashion. We derive the conserved quantities associated with the latter and show that the mapping class group of the surface acts on the phase space via Poisson isomorphisms
Effective Chern-Simons actions of particles coupled to 3D gravity
Trześniewski, Tomasz
2018-03-01
Point particles in 3D gravity are known to behave as topological defects, while gravitational field can be expressed as the Chern-Simons theory of the appropriate local isometry group of spacetime. In the case of the Poincaré group, integrating out the gravitational degrees of freedom it is possible to obtain the effective action for particle dynamics. We review the known results, both for single and multiple particles, and attempt to extend this approach to the (anti-)de Sitter group, using the factorizations of isometry groups into the double product of the Lorentz group and AN (2) group. On the other hand, for the de Sitter group one can also perform a contraction to the semidirect product of AN (2) and the translation group. The corresponding effective action curiously describes a Carrollian particle with the AN (2) momentum space. We derive this contraction in a more rigorous manner and further explore its properties, including a generalization to the multiparticle case.
Ye, Fei; Marchetti, P. A.; Su, Z. B.; Yu, L.
2017-09-01
The relation between braid and exclusion statistics is examined in one-dimensional systems, within the framework of Chern-Simons statistical transmutation in gauge invariant form with an appropriate dimensional reduction. If the matter action is anomalous, as for chiral fermions, a relation between braid and exclusion statistics can be established explicitly for both mutual and nonmutual cases. However, if it is not anomalous, the exclusion statistics of emergent low energy excitations is not necessarily connected to the braid statistics of the physical charged fields of the system. Finally, we also discuss the bosonization of one-dimensional anyonic systems through T-duality. Dedicated to the memory of Mario Tonin.
Hassaine, Mokhtar
2016-01-01
This book grew out of a set of lecture notes on gravitational Chern–Simons (CS) theories developed over the past decade for several schools and different audiences including graduate students and researchers.CS theories are gauge-invariant theories that can include gravity consistently. They are only defined in odd dimensions and represent a very special class of theories in the Lovelock family. Lovelock gravitation theories are the natural extensions of General Relativity for dimensions greater than four that yield second-order field equations for the metric. These theories also admit local supersymmetric extensions where supersymmetry is an off-shell symmetry of the action, as in a standard gauge theory.Apart from the arguments of mathematical elegance and beauty, the gravitational CS actions are exceptionally endowed with physical attributes that suggest the viability of a quantum interpretation. CS theories are gauge-invariant, scale-invariant and background independent; they have no dimensional couplin...
Linearized fermion-gravitation system in a (2+1)-dimensional space-time with Chern-Simons data
International Nuclear Information System (INIS)
Mello, E.R.B. de.
1990-01-01
The fermion-graviton system at linearized level in a (2+1)-dimensional space-time with the gravitational Chern-Simons term is studied. In this approximation it is shown that this system presents anomalous rotational properties and spin, in analogy with the gauge field-matter system. (A.C.A.S.) [pt
Finite action for Chern-Simons Ads gravity
Energy Technology Data Exchange (ETDEWEB)
Mora, P.; Olea, R.; Troncoso, R.; Zanelli, J. E-mail: jz@cecs.cl
2004-06-01
A finite principle for Chern-Simons AdS gravity is presented. The construction is carried out in detail first in five dimensions, where the bulk action is given by a particular combination of the Einstein-Hilbert action with negative cosmological constant and a Gauss-Bonnet term; and is then generalized for arbitrary odd dimensions. The boundary term needed to render the action finite is singled out demanding the action to attain an extremum for an appropriate set of boundary conditions. The boundary term is a local function of the fields at the boundary and is sufficient to render the action finite for asymptotically AdS solutions, without requiring background fields. It is shown that the Euclidean continuation of the action correctly describes black hole thermodynamics in the canonical ensemble. Additionally, background independent conserved charges associated with the asymptotic symmetries can be written as surface integrals by direct application of Noether's theorem. (author)
Possible daily and seasonal variations in quantum interference induced by Chern-Simons gravity.
Okawara, Hiroki; Yamada, Kei; Asada, Hideki
2012-12-07
Possible effects of Chern-Simons (CS) gravity on a quantum interferometer turn out to be dependent on the latitude and direction of the interferometer on Earth in orbital motion around the Sun. Daily and seasonal variations in phase shifts are predicted with an estimate of the size of the effects, wherefore neutron interferometry with ~5 m arm length and ~10(-4) phase measurement accuracy would place a bound on a CS parameter comparable to the Gravity Probe B satellite.
A Chern-Simons gauge-fixed Lagrangian in a 'non-canonical' BRST approach
International Nuclear Information System (INIS)
Constantinescu, R; Ionescu, C
2009-01-01
This paper presents a possible path which starts from the extended BRST Hamiltonian formalism and ends with a covariant Lagrangian action, using the equivalence between the two formalisms. The approach allows a simple account of the form of the master equation and offers a natural identification of some 'non-canonical' operators and variables. These are the main items which solve the major difficulty of the extended BRST Lagrangian formalism, i.e., the gauge-fixing problem. The algorithm we propose applies to a non-Abelian Chern-Simons model coupled with Dirac fields
N=2-Maxwell-Chern-Simons model with anomalous magnetic moment coupling via dimensional reduction
International Nuclear Information System (INIS)
Christiansen, H.R.; Cunha, M.S.; Helayel Neto, Jose A.; Manssur, L.R.U; Nogueira, A.L.M.A.
1998-02-01
An N=1-supersymmetric version of the Cremmer-Scherk-Kalb-Ramond model with non-minimal coupling to matter is built up both in terms of superfields and in a component field formalism. By adopting a dimensional reduction procedure, the N=2-D=3 counterpart of the model comes out, with two main features: a genuine (diagonal) Chern-Simons term and an anomalous magnetic moment coupling between matter and the gauge potential. (author)
Ghosh, K. J. B.; Klinkhamer, F. R.
2018-01-01
We consider four-dimensional chiral gauge theories defined over a spacetime manifold with topology R3 ×S1 and periodic boundary conditions over the compact dimension. The effective gauge-field action is calculated for Abelian U (1) gauge fields Aμ (x) which depend on all four spacetime coordinates (including the coordinate x4 ∈S1 of the compact dimension) and have vanishing components A4 (x) (implying trivial holonomies in the 4-direction). Our calculation shows that the effective gauge-field action contains a local Chern-Simons-like term which violates Lorentz and CPT invariance. This result is established perturbatively with a generalized Pauli-Villars regularization and nonperturbatively with a lattice regularization based on Ginsparg-Wilson fermions.
Dimensional reduction of U(1) x SU(2) Chern-Simons bosonization: Application to the t - J model
International Nuclear Information System (INIS)
Marchetti, P.A.
1996-09-01
We perform a dimensional reduction of the U(1) x SU(2) Chern-Simons bosonization and apply it to the t - J model, relevant for high T c superconductors. This procedure yields a decomposition of the electron field into a product of two ''semionic'' fields, i.e. fields obeying Abelian braid statistics with statistics parameter θ = 1/4, one carrying the charge and the other the spin degrees of freedom. A mean field theory is then shown to reproduce correctly the large distance behaviour of the correlation functions of the 1D t - J model at >> J. This result shows that to capture the essential physical properties of the model one needs a specific ''semionic'' form of spin-charge separation. (author). 31 refs
On the role of the Chern-Simons action for the description of the QHE
International Nuclear Information System (INIS)
Cabo, A.; Oliva, D.
1990-05-01
The role of the Chern-Simons action in the description of the quantum Hall effects is stressed. The 2D-electromagnetic picture of Widom and Srivastava is shown to be valid in a superlattice of 2D-electron gases. A Meissner-like effect appears in such systems. In them, the difference between the external and the integer filling factor fields is exponentially screened by the surface (edge) currents. Also, effective Maxwell equations for one sheet or a superlattice are obtained. (author). 21 refs
Inducing the μ and the Bμ term by the radion and the 5d Chern-Simons term
International Nuclear Information System (INIS)
Hebecker, A.; March-Russell, J.; Ziegler, R.
2009-01-01
In 5-dimensional models with gauge-Higgs unification, the F-term vacuum expectation value of the radion provides, in close analogy to the Giudice-Masiero mechanism, a natural source for the μ and Bμ term. Both the leading order gauge theory lagrangian and the supersymmetric Chern-Simons term contain couplings to the radion superfield which can be used for this purpose. We analyse the basic features of this mechanism for μ term generation and provide an explicit example, based on a variation of the SU(6) gauge-Higgs unification model of Burdman and Nomura. This construction contains all the relevant features used in our generic analysis. More generally, we expect our mechanism to be relevant to many of the recently discussed orbifold GUT models derived from heterotic string theory. This provides an interesting way of testing high-scale physics via Higgs mass patterns accessible at the LHC.
International Nuclear Information System (INIS)
Sourrouille, Lucas; Casana, Rodolfo
2016-01-01
We have studied the existence of self-dual solitonic solutions in a generalization of the Abelian Chern-Simons-Higgs model. Such a generalization introduces two different nonnegative functions, ω_1(|ϕ|) and ω(|ϕ|), which split the kinetic term of the Higgs field, |D_μϕ|"2→ω_1(|ϕ|)|D_0ϕ|"2-ω(|ϕ|)|D_kϕ|"2, breaking explicitly the Lorentz covariance. We have shown that a clean implementation of the Bogomolnyi procedure only can be implemented whether ω(|ϕ|)∝β|ϕ|"2"β"-"2 with β≥1. The self-dual or Bogomolnyi equations produce an infinity number of soliton solutions by choosing conveniently the generalizing function ω_1(|ϕ|) which must be able to provide a finite magnetic field. Also, we have shown that by properly choosing the generalizing functions it is possible to reproduce the Bogomolnyi equations of the Abelian Maxwell-Higgs and Chern-Simons-Higgs models. Finally, some new self-dual |ϕ|"6-vortex solutions have been analyzed from both theoretical and numerical point of view.
Relativistic particles coupled to Chern-Simons term-revisited
International Nuclear Information System (INIS)
Chakraborty, B.
1995-01-01
The author considers the model of N relativistic spinless particles coupled to an abelian Chern-Simons term. Rewriting the action in a time reparamaterized form by introducing an arbitary parameter, parameterizing the world line of the particles, the author makes a classical constraint Hamiltonian analysis of the model. Subsequent to gauge fixing by equating the arbitrary parameter with the time the author identifies the Hamiltonian of the system, which agrees with the Hamiltonian obtained by using Banerjee's method of fixing the arbitrary Langrange multiplier by using equations of motion. The author exhibits the Poincare invariance of the model, at the classical level, by constructing spacetime generators using either the canonical or symmetric definition of the energy-momentum tensor. A detailed comparison of the expressions of angular momentum obtained by both methods show that both agree up to a boundary term. In presence of rotationally symmetric vortex configuration this term can be interpreted as an anomalous angular momentum term. The author also heuristically discusses the effect of gauge fixing on the transformation properties. 13 refs
N = 1 super-Chern-Simons coupled to parity-preserving matter from Atiyah-Ward space-time
International Nuclear Information System (INIS)
Andrade, M.A. de; Cima, O.M. Del; Colatto, L.P.
1995-06-01
In this letter, we present the Parkes-Siegel formulation for the massive Abelian N=1 super-QED 2+2 coupled to a self-dual supermultiplet, by introducing a chiral multiplier superfield. We show that after carrying out a suitable dimensional reduction from (2+2) to (1+2) dimensions, and performing some necessary truncations, the simple supersymmetric extension of the π3 QED 1+2 coupled to a Chern-Simons term naturally comes out. (author). 15 refs
Abelian gauge theories on homogeneous spaces
International Nuclear Information System (INIS)
Vassilevich, D.V.
1992-07-01
An algebraic technique of separation of gauge modes in Abelian gauge theories on homogeneous spaces is proposed. An effective potential for the Maxwell-Chern-Simons theory on S 3 is calculated. A generalization of the Chern-Simons action is suggested and analysed with the example of SU(3)/U(1) x U(1). (author). 11 refs
Maxwell-Chern-Simons vortices in a CPT-odd Lorentz-violating Higgs electrodynamics
International Nuclear Information System (INIS)
Casana, R.; Ferreira, M.M.; Hora, E. da; Neves, A.B.F.
2014-01-01
We study BPS vortices in a CPT-odd and Lorentz-violating Maxwell-Chern-Simons-Higgs (MCSH) electrodynamics attained from the dimensional reduction of the Carroll-Field-Jackiw-Higgs model. The Lorentz-violating parameter induces a pronounced behavior at origin (for the magnetic/electric fields and energy density) which is absent in the MCSH vortices. For some combination of the Lorentz-violating coefficients there always exists a sufficiently large winding number n 0 such that for all vertical stroke n vertical stroke ≥ vertical stroke n 0 vertical stroke the magnetic field flips sign, yielding two well-defined regions with opposite magnetic flux. However, the total magnetic flux remains quantized and proportional to the winding number. (orig.)
Dynamics of magnetic fields in Maxwell, Yang-Mills and Chern-Simons theories on the torus
International Nuclear Information System (INIS)
Burgess, M.; McLachlan, A.; Toms, D.J.
1992-01-01
The problem of uniform magnetic fields passing perpendicularly through a 2-torus, Abelian and Non-Abelian, is considered. Focus is on dynamical effects of non-integrable phases on the torus at non zero B and from magnetic fields themselves in the vacuum. The spectrum is computed and is shown to be always independent of the non-integrable phases on the torus. It is concluded that a Chern-Simons term will always be induced by radiative corrections to fermions on the torus when B ≠ 0. The special case of an electromagnetically uncharged anyon gas in noted and shown to be a system whose spectrum can depend on the non-integrable phases in the two torus directions, subject to a consistency requirement. In three and four dimensions, dynamical symmetry breaking of non-Abelian fields and associated condensate formation is possible by radiative corrections. The classification on non-Abelian magnetic fields in terms of ''flux integers'' is discussed, and a method for obtaining such integers for an arbitrary gauge algebra is presented. This provides a rigorous generalisation of Hooft's su (2) classification. 72 refs., 5 figs
International Nuclear Information System (INIS)
Menezes, G.; Svaiter, N.F.
2006-04-01
We use the method of stochastic quantization in a topological field theory defined in an Euclidean space, assuming a Langevin equation with a memory kernel. We show that our procedure for the Abelian Chern-Simons theory converges regardless of the nature of the Chern-Simons coefficient. (author)
A Relation Between Topological Quantum Field Theory and the Kodama State
Oda, Ichiro
2003-01-01
We study a relation between topological quantum field theory and the Kodama (Chern-Simons) state. It is shown that the Kodama (Chern-Simons) state describes a topological state with unbroken diffeomorphism invariance in Yang-Mills theory and Einstein's general relativity in four dimensions. We give a clear explanation of "why" such a topological state exists.
Quest for Casimir repulsion between Chern-Simons surfaces
Fialkovsky, Ignat; Khusnutdinov, Nail; Vassilevich, Dmitri
2018-04-01
In this paper we critically reconsider the Casimir repulsion between surfaces that carry the Chern-Simons interaction (corresponding to the Hall-type conductivity). We present a derivation of the Lifshitz formula valid for arbitrary planar geometries and discuss its properties. This analysis allows us to resolve some contradictions in the previous literature. We compute the Casimir energy for two surfaces that have constant longitudinal and Hall conductivities. The repulsion is possible only if both surfaces have Hall conductivities of the same sign. However, there is a critical value of the longitudinal conductivity above which the repulsion disappears. We also consider a model where both parity odd and parity even terms in the conductivity are produced by the polarization tensor of surface modes. In contrast to the previous publications [L. Chen and S.-L. Wan, Phys. Rev. B 84, 075149 (2011), 10.1103/PhysRevB.84.075149; Phys. Rev. B 85, 115102 (2012), 10.1103/PhysRevB.85.115102], we include the parity anomaly term. This term ensures that the conductivities vanish for infinitely massive surface modes. We find that at least for a single mode, regardless of the sign and value of its mass, there is no Casimir repulsion.
Once more about the topologically massive gauge theory
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Kogan, Ya.I.
1989-01-01
The general properties of the three-dimensional gauge theory with the topological mass is discussed namely the long-range interaction of the Aharonov-Bohm type. It is argued that Chern-Simons gauge theories must be considered as the infrared limit of the topologically massive theories. The analogy between the Landau problem of a charged particle in a magnetic field and quantization of this gauge theory is considered, as well as the quantization condition for the Abelian Chern-Simons term. 38 refs.; 5 figs
Thin accretion disk signatures in dynamical Chern-Simons-modified gravity
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Harko, Tiberiu; Kovacs, Zoltan; Lobo, Francisco S N
2010-01-01
A promising extension of general relativity is Chern-Simons (CS)-modified gravity, in which the Einstein-Hilbert action is modified by adding a parity-violating CS term, which couples to gravity via a scalar field. In this work, we consider the interesting, yet relatively unexplored, dynamical formulation of CS-modified gravity, where the CS coupling field is treated as a dynamical field, endowed with its own stress-energy tensor and evolution equation. We consider the possibility of observationally testing dynamical CS-modified gravity by using the accretion disk properties around slowly rotating black holes. The energy flux, temperature distribution, the emission spectrum as well as the energy conversion efficiency are obtained, and compared to the standard general relativistic Kerr solution. It is shown that the Kerr black hole provides a more efficient engine for the transformation of the energy of the accreting mass into radiation than their slowly rotating counterparts in CS-modified gravity. Specific signatures appear in the electromagnetic spectrum, thus leading to the possibility of directly testing CS-modified gravity by using astrophysical observations of the emission spectra from accretion disks.
U(1) x SU(2) Chern-Simons gauge theory of underdoped cuprate superconductors
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Marchetti, P.A.; Su Zhao-Bin; Yu Lu
1998-05-01
The Chern-Simons bosonization with U(1)xSU(2) gauge field is applied to the 2-D t-J model in the limit t>>J, to study the normal state properties of underdoped cuprate superconductors. We prove the existence of an upper bound on the partition function for holons in a spinon background, and we find the optimal spinon configuration saturating the upper bound on average - a coexisting flux phase and s+id-like RVB state. After neglecting the feedback of holon fluctuations on the U(1) field B and spinon fluctuations on the SU(2) field V, the holon field is a fermion and the spinon field is a hard-core boson. Within this approximation we show that the B field produces a π flux phase for the holons, converting them into Dirac-like fermions, while the V field, taking into account the feedback of holons produces a gap for the spinons vanishing in the zero doping limit. The nonlinear σ-model with a mass term describes the crossover from the short-ranged antiferromagnetic (AF) state in doped samples to long range AF order in reference compounds. Moreover, we derive a low-energy effective action in terms of spinons holons and a self-generated U(1) gauge field. Neglecting the gauge fluctuations, the holons are described by the Fermi liquid theory with a Fermi surface consisting of 4 ''half-pockets'' centered at (+-π/2,+-π/2) and one reproduces the results for the electron spectral function obtained in the mean field approximation, in agreement with the photoemission data on underdoped cuprates. The gauge fluctuations are not confining due to coupling to holons, but nevertheless yield an attractive interaction between spinons and holons leading to a bound state with electron quantum numbers. The renormalisation effects due to gauge fluctuations give rise to non-Fermi liquid behaviour for the composite electron, in certain temperature range showing the linear in T resistivity. This formalism provides a new interpretation of the spin gap in the underdoped superconductors
Chern–Simons theory in SIM(1) superspace
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Vohánka, Jiří; Faizal, Mir
2015-01-01
In this paper, we will analyze a three-dimensional supersymmetric Chern–Simons theory in SIM(1) superspace formalism. The breaking of the Lorentz symmetry down to the SIM(1) symmetry breaks half the supersymmetry of the Lorentz invariant theory. So, the supersymmetry of the Lorentz invariant Chern–Simons theory with N=1 supersymmetry will break down to N=1/2 supersymmetry, when the Lorentz symmetry is broken down to the SIM(1) symmetry. First, we will write the Chern–Simons action using SIM(1) projections of N=1 superfields. However, as the SIM(1) transformations of these projections are very complicated, we will define SIM(1) superfields which transform simply under SIM(1) transformations. We will then express the Chern–Simons action using these SIM(1) superfields. Furthermore, we will analyze the gauge symmetry of this Chern–Simons theory. This is the first time that a Chern–Simons theory with N=1/2 supersymmetry will be constructed on a manifold without a boundary
Does the Higgs mechanism favour electron-electron bound states in Maxwell-Chern-Simons QED3?
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Belich, Humberto; Helayeel-Neto, Jose Abdalla; Ferreira Junior, Manoel Messias
2000-01-01
Full text follows: We show that low-energy electron-electron bound states appear in the Maxwell-Chern-Simons (MCS) planar QED. In spite of the repulsive interaction mediated by the MCS gauge field, a net attractive interaction stems due to the Higgs mechanism through an Yukawa-type interaction. The spontaneous breaking of a local U(1)-symmetry is realized by a γ 6 -type potential. We conclude, by using the Schroedinger equation associated to the net attractive scattering potential, that electron-electron bound states arise in the model. Therefore, the Higgs mechanism overcomes the difficulties found out by Girotti et al. (Phys. Rev. Lett. 69 (1992) 2623) in searching for bound states in the MCS planar QED. (author)
Energy Technology Data Exchange (ETDEWEB)
Bartolo, Nicola; Orlando, Giorgio, E-mail: nicola.bartolo@pd.infn.it, E-mail: giorgio.orlando@phd.unipd.it [Dipartimento di Fisica e Astronomia ' ' G. Galilei' , Università degli Studi di Padova, via Marzolo 8, 35131, Padova (Italy)
2017-07-01
Considering high-energy modifications of Einstein gravity during inflation is an interesting issue. We can constrain the strength of the new gravitational terms through observations of inflationary imprints in the actual universe. In this paper we analyze the effects on slow-roll models due to a Chern-Simons term coupled to the inflaton field through a generic coupling function f (φ). A well known result is the polarization of primordial gravitational waves (PGW) into left and right eigenstates, as a consequence of parity breaking. In such a scenario the modifications to the power spectrum of PGW are suppressed under the conditions that allow to avoid the production of ghost gravitons at a certain energy scale, the so-called Chern-Simons mass M {sub CS}. In general it has been recently pointed out that there is very little hope to efficiently constrain chirality of PGW on the basis solely of two-point statistics from future CMB data, even in the most optimistic cases. Thus we search if significant parity breaking signatures can arise at least in the bispectrum statistics. We find that the tensor-tensor-scalar bispectra ( γ γ ζ ) for each polarization state are the only ones that are not suppressed. Their amplitude, setting the level of parity breaking during inflation, is proportional to the second derivative of the coupling function f (φ) and they turn out to be maximum in the squeezed limit. We comment on the squeezed-limit consistency relation arising in the case of chiral gravitational waves, and on possible observables to constrain these signatures.
Large data well-posedness in the energy space of the Chern-Simons-Schrödinger system
Lim, Zhuo Min
2018-02-01
We consider the initial-value problem for the Chern-Simons-Schrödinger system, which is a gauge-covariant Schrödinger system in Rt × Rx2 with a long-range electromagnetic field. We show that, in the Coulomb gauge, it is locally well-posed in Hs for s ⩾ 1, and the solution map satisfies a local-in-time weak Lipschitz bound. By energy conservation, we also obtain a global regularity result. The key is to retain the non-perturbative part of the derivative nonlinearity in the principal operator, and exploit the dispersive properties of the resulting paradifferential-type principal operator using adapted Up and Vp spaces.
Medium generated gap in gravity and a 3D gauge theory
Gabadadze, Gregory; Older, Daniel
2018-05-01
It is well known that a physical medium that sets a Lorentz frame generates a Lorentz-breaking gap for a graviton. We examine such generated "mass" terms in the presence of a fluid medium whose ground state spontaneously breaks spatial translation invariance in d =D +1 spacetime dimensions, and for a solid in D =2 spatial dimensions. By requiring energy positivity and subluminal propagation, certain constraints are placed on the equation of state of the medium. In the case of D =2 spatial dimensions, classical gravity can be recast as a Chern-Simons gauge theory, and motivated by this we recast the massive theory of gravity in AdS3 as a massive Chern-Simons gauge theory with an unusual mass term. We find that in the flat space limit the Chern-Simons theory has a novel gauge invariance that mixes the kinetic and mass terms, and enables the massive theory with a noncompact internal group to be free of ghosts and tachyons.
I-Love-Q relations for neutron stars in dynamical Chern Simons gravity
Gupta, Toral; Majumder, Barun; Yagi, Kent; Yunes, Nicolás
2018-01-01
Neutron stars are ideal to probe, not only nuclear physics, but also strong-field gravity. Approximate universal relations insensitive to the star’s internal structure exist among certain observables and are useful in testing general relativity, as they project out the uncertainties in the equation of state. One such set of universal relations between the moment of inertia (I), the tidal Love number and the quadrupole moment (Q) has been studied both in general relativity and in modified theories. In this paper, we study the relations in dynamical Chern–Simons gravity, a well-motivated, parity-violating effective field theory, extending previous work in various ways. First, we study how projected constraints on the theory using the I-Love relation depend on the measurement accuracy of I with radio observations and that of the Love number with gravitational-wave observations. Provided these quantities can be measured with future observations, we find that the latter could place bounds on dynamical Chern–Simons gravity that are six orders of magnitude stronger than current bounds. Second, we study the I–Q and Q-Love relations in this theory by constructing slowly-rotating neutron star solutions to quadratic order in spin. We find that the approximate universality continues to hold in dynamical Chern–Simons gravity, and in fact, it becomes stronger than in general relativity, although its existence depends on the normalization of the dimensional coupling constant of the theory. Finally, we study the variation of the eccentricity of isodensity contours inside a star and its relation to the degree of universality. We find that, in most cases, the eccentricity variation is smaller in dynamical Chern–Simons gravity than in general relativity, providing further support to the idea that the approximate self-similarity of isodensity contours is responsible for universality.
Jejjala, Vishnumohan
2002-01-01
makes falsifiable predictions about TeV scale physics. Susskind has proposed that the fractional quantum Hall system can be realized through an Abelian Chern-Simons theory with a Moyal product. Susskind's Chern-Simons field is a hydrodynamical quantity. Lopez and Fradkin have an alternate Chern-Simons description couched in terms of a statistical gauge field. We show that this statistical Chern-Simons theory also possesses a non-commutative structure and develop the dictionary between the two Chern-Simons pictures.
Framing anomaly in the effective theory of the fractional quantum Hall effect.
Gromov, Andrey; Cho, Gil Young; You, Yizhi; Abanov, Alexander G; Fradkin, Eduardo
2015-01-09
We consider the geometric part of the effective action for the fractional quantum Hall effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to obtain the correct gravitational linear response functions. In the lowest order in gradients, the linear response generating functional includes Chern-Simons, Wen-Zee, and gravitational Chern-Simons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and contributes to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses for non-Abelian FQH states.
Moduli space of Chern-Simons gravity
International Nuclear Information System (INIS)
Soda, Jiro; Yamanaka, Yuki
1990-09-01
Conformally invariant (2+1)-dimensional gravity, Chern-Shimons gravity, is studied. Its solution space, moduli space, is investigated using the linearization method. The dimension of moduli space is determined as 18g - 18 for g > 1,6 for g = 1 and 0 for g = 0. We discuss the geometrical meaning of our investigation. (author)
Topological field theory and surgery on three-manifolds
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Guadagnini, E.; Panicucci, S.
1992-01-01
The solution of the SU(2) quantum Chern-Simons field theory defined on a closed, connected and orientable three-manifold is presented. The vacuum expectation values of Wilson line operators, associated with framed links in a generic manifold, are computed in terms of the expectation values of the three-sphere. The method consists of using an operator realization of Dehn surgery. The rules, corresponding to the surgery instructions in the three-sphere, are derived and the three-manifold invariant defined by the Chern-Simons theory is constructed. Several examples are considered and explicit results are reported. (orig.)
Topological resolution of gauge theory singularities
Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo
2013-08-01
Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric SU(2) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.
Topological resolution of gauge theory singularities
Energy Technology Data Exchange (ETDEWEB)
Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo
2013-08-21
Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric S U ( 2 ) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.
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Kamiya, Noriaki; Sato, Matsuo
2014-01-01
We define Hermitian (ϵ,δ)-Freudenthal-Kantor triple systems and prove a structure theorem. We also give some examples of triple systems that are generalizations of the u(N)⊕u(M) and sp(2N)⊕u(1) Hermitian 3-algebras. We apply a *-generalized Jordan triple system to a field theory and obtain a Chern-Simons gauge theory. We find that the novel Higgs mechanism works, where the Chern-Simons gauge theory reduces to a Yang-Mills theory in a certain limit
Huang, Yu-tin; Johansson, Henrik
2013-04-26
We show that three-dimensional supergravity amplitudes can be obtained as double copies of either three-algebra super-Chern-Simons matter theory or two-algebra super-Yang-Mills theory when either theory is organized to display the color-kinematics duality. We prove that only helicity-conserving four-dimensional gravity amplitudes have nonvanishing descendants when reduced to three dimensions, implying the vanishing of odd-multiplicity S-matrix elements, in agreement with Chern-Simons matter theory. We explicitly verify the double-copy correspondence at four and six points for N = 12,10,8 supergravity theories and discuss its validity for all multiplicity.
High energy instanton induced processes in electroweak theory
International Nuclear Information System (INIS)
McLerran, L.
1992-01-01
It is well known that in electroweak theory, baryon plus lepton number is conserved by the classical equations of motion. This is of course consistent with the lack of experimental observation of such processes. It is a little less well known that when quantum corrections are included in electroweak theory, baryon plus lepton number is not conserved. This was first discovered as a consequence of the Adler-Bardeen-Bell-Jackiw triangle anomaly. It is perhaps most easily understood as a consequence of vacuum degeneracy, fermion energy level crossing and filling of the negative energy Dirac sea upon second quantization. To understand how baryon plus lepton number is not conserved upon second quantization, consider the situation shown in the energy of the system is shown as a function of a parameter which characterizes the gauge fields, the Chern-Simons charge. The Chern-Simons charge is a function only of the gauge fields, and the B + L change is equal to the change in Chern-Simons charge, ΔQ B+L = ΔQ CS
String theory duals of Lifshitz–Chern–Simons gauge theories
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Balasubramanian, Koushik; McGreevy, John
2012-01-01
We propose candidate gravity duals for a class of non-Abelian z = 2 Lifshitz Chern–Simons (LCS) gauge theories studied by Mulligan, Kachru and Nayak. These are nonrelativistic gauge theories in 2+1 dimensions in which parity and time-reversal symmetries are explicitly broken by the presence of a Chern–Simons term. We show that these field theories can be realized as deformations of DLCQ N=4 super Yang–Mills theory. Using the holographic dictionary, we identify the bulk fields of type IIB supergravity that are dual to these deformations. The geometries describing the groundstates of the non-Abelian LCS gauge theories realized here exhibit a mass gap. (paper)
Beyond Lovelock gravity: Higher derivative metric theories
Crisostomi, M.; Noui, K.; Charmousis, C.; Langlois, D.
2018-02-01
We consider theories describing the dynamics of a four-dimensional metric, whose Lagrangian is diffeomorphism invariant and depends at most on second derivatives of the metric. Imposing degeneracy conditions we find a set of Lagrangians that, apart form the Einstein-Hilbert one, are either trivial or contain more than 2 degrees of freedom. Among the partially degenerate theories, we recover Chern-Simons gravity, endowed with constraints whose structure suggests the presence of instabilities. Then, we enlarge the class of parity violating theories of gravity by introducing new "chiral scalar-tensor theories." Although they all raise the same concern as Chern-Simons gravity, they can nevertheless make sense as low energy effective field theories or, by restricting them to the unitary gauge (where the scalar field is uniform), as Lorentz breaking theories with a parity violating sector.
International Nuclear Information System (INIS)
Mansouri, F.; Suranyi, P.; Wijewardhana, L.C.R.
1992-10-01
Dynamics of 2+1 dimensional gravity is analyzed by coupling matter to Chern Simons Witten action in two ways and obtaining the exact gravity Hamiltonian for each case. 't Hoot's Hamiltonian is obtained as an approximation. The notion of space-time emerges in the very end as a broken phase of the gauge theory. We have studied the patterns of discrete and continuous symmetry breaking in 2+1 dimensional field theories. We formulate our analysis in terms of effective composite scalar field theories. Point-like sources in the Chern-Simons theory of gravity in 2+1 dimensions are described by their Poincare' charges. We have obtained exact solutions of the constraints of Chern-Simons theory with an arbitrary number of isolated point sources in relative motion. We then showed how the space-time metric is constructed. A reorganized perturbation expansion with a propagator of soft infrared behavior has been used to study the critical behavior of the mass gap. The condition of relativistic covariance fixes the form of the soft propagator. Approximants to the correlation critical exponent were obtained in two loop order for the two and three dimensional theories. We proposed a new model of QED exhibiting two phases and a Majorana mass spectrum of single particle states. The model has a new source of coupling constant renormalization which opposes screening and suggests the model may confine. Assuming that the bound states of e + e - essentially obey a Majorana spectrum, we obtained a consistent fit of the GSI peaks as well as predicting new peaks and their spin assignments
Cosmological Analysis of Dynamical Chern-Simons Modified Gravity via Dark Energy Scenario
Directory of Open Access Journals (Sweden)
Abdul Jawad
2015-01-01
Full Text Available The purpose of this paper is to study the cosmological evolution of the universe in the framework of dynamical Chern-Simons modified gravity. We take pilgrim dark energy model with Hubble and event horizons in interacting scenario with cold dark matter. For this scenario, we discuss cosmological parameters such as Hubble and equation of state and cosmological plane like ωϑ-ωϑ′ and squared speed of sound. It is found that Hubble parameter approaches the ranges 75-0.5+0.5 (for u=2 and (74, 74.30 (for u=1,-1,-2 for Hubble horizon pilgrim dark energy. It implies the ranges 74.80-0.005+0.005 (for u=2 and (73.4, 74 (for u=-2 for event horizon pilgrim dark energy. The equation of state parameter provides consistent ranges with different observational schemes. Also, ωϑ-ωϑ′ planes lie in the range (ωϑ=-1.13-0.25+0.24,ωϑ′<1.32. The squared speed of sound shows stability for all present models in the present scenario. We would like to mention here that our results of various cosmological parameters show consistency with different observational data like Planck, WP, BAO, H0, SNLS, and WMAP.
The Chern-Simons current in time series of knots and links in proteins
Capozziello, Salvatore; Pincak, Richard
2018-06-01
A superspace model of knots and links for DNA time series data is proposed to take into account the feedback loop from docking to undocking state of protein-protein interactions. In particular, the direction of interactions between the 8 hidden states of DNA is considered. It is a E8 ×E8 unified spin model where the genotype, from active and inactive side of DNA time data series, can be considered for any living organism. The mathematical model is borrowed from loop-quantum gravity and adapted to biology. It is used to derive equations for gene expression describing transitions from ground to excited states, and for the 8 coupling states between geneon and anti-geneon transposon and retrotransposon in trash DNA. Specifically, we adopt a modified Grothendieck cohomology and a modified Khovanov cohomology for biology. The result is a Chern-Simons current in (8 + 3) extradimensions of a given unoriented supermanifold with ghost fields of protein structures. The 8 dimensions come from the 8 hidden states of spinor field of genetic code. The extradimensions come from the 3 types of principle fiber bundle in the secondary protein.
Monopole Solutions in Topologically Massive Gauge Theory
International Nuclear Information System (INIS)
Teh, Rosy; Wong, Khai-Ming; Koh, Pin-Wai
2010-01-01
Monopoles in topologically massive SU(2) Yang-Mils-Higgs gauge theory in 2+1 dimensions with a Chern-Simon mass term have been studied by Pisarski some years ago. He argued that there is a monopole solution that is regular everywhere, but found that it does not possess finite action. There were no exact or numerical solutions being presented by him. Hence it is our purpose to further investigate this solution in more detail. We obtained numerical regular solutions that smoothly interpolates between the behavior at small and large distances for different values of Chern-Simon term strength and for several fixed values of Higgs field strength.
Spatially modulated instabilities of holographic gauge-gravitational anomaly
Energy Technology Data Exchange (ETDEWEB)
Liu, Yan [Department of Space Science, and International Research Institute of Multidisciplinary Science,Beihang University,Beijing 100191 (China); Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid,Cantoblanco, 28049 Madrid (Spain); Pena-Benitez, Francisco [Dipartimento di Fisica, Università di Perugia, I.N.F.N. Sezione di Perugia,Via A. Pascoli, I-06123 Perugia (Italy)
2017-05-19
We performed a study of the perturbative instabilities in Einstein-Maxwell-Chern-Simons theory with a gravitational Chern-Simons term, which is dual to a strongly coupled field theory with both chiral and mixed gauge-gravitational anomaly. With an analysis of the fluctuations in the near horizon regime at zero temperature, we found that there might be two possible sources of instabilities. The first one corresponds to a real mass-squared which is below the BF bound of AdS{sub 2}, and it leads to the bell-curve phase diagram at finite temperature. The effect of mixed gauge-gravitational anomaly is emphasised. Another source of instability is independent of gauge Chern-Simons coupling and exists for any finite gravitational Chern-Simons coupling. There is a singular momentum close to which unstable mode appears. The possible implications of this singular momentum are discussed. Our analysis suggests that the theory with a gravitational Chern-Simons term around Reissner-Nordström black hole is unreliable unless the gravitational Chern-Simons coupling is treated as a small perturbative parameter.
Wigner's little group as a gauge generator in linearized gravity theories
International Nuclear Information System (INIS)
Scaria, Tomy; Chakraborty, Biswajit
2002-01-01
We show that the translational subgroup of Wigner's little group for massless particles in 3 + 1 dimensions generates gauge transformation in linearized Einstein gravity. Similarly, a suitable representation of the one-dimensional translational group T(1) is shown to generate gauge transformation in the linearized Einstein-Chern-Simons theory in 2 + 1 dimensions. These representations are derived systematically from appropriate representations of translational groups which generate gauge transformations in gauge theories living in spacetime of one higher dimension by the technique of dimensional descent. The unified picture thus obtained is compared with a similar picture available for vector gauge theories in 3 + 1 and 2 + 1 dimensions. Finally, the polarization tensor of the Einstein-Pauli-Fierz theory in 2 + 1 dimensions is shown to split into the polarization tensors of a pair of Einstein-Chern-Simons theories with opposite helicities suggesting a doublet structure for the Einstein-Pauli-Fierz theory
International Nuclear Information System (INIS)
Moore, G.; Seiberg, N.
1989-01-01
All known rational conformal field theories may be obtained from (2+1)-dimensional Chern-Simons gauge theories by appropriate choice of gauge group. We conjecture that all rational field theories are classified by groups via (2+1)-dimensional Chern-Simons gauge theories. (orig.)
International Nuclear Information System (INIS)
Battistel, O.A.; Dallabona, G.
2004-01-01
We consider the possible role played by the anomaly cancellation mechanism in the evaluation of the radiatively induced Chern-Simons (CS) term, arising from the Lorentz and CPT non-invariant fermionic sector, of an extended version of QED. We explicit evaluate the most general mathematical structure associated to the AVV triangle amplitude, closely related to the one involved in the CS term evaluation, using for this purposes an alternative calculational strategy to handle divergences in QFT's. We show that the requirement of consistency with the choices made in the construction of the Standard Model's renormalizability, in the evaluation of the AVV Green function, leave no room for a nonvanishing radiatively induced CS term, independently of the regularization prescription or equivalent philosophy adopted, in accordance with what was previously conjectured by other authors. (orig.)
Comments on Dirac-like monopole, Maxwell and Maxwell-Chern-Simons electrodynamics in D=(2+1)
Energy Technology Data Exchange (ETDEWEB)
Moura-Melo, Winder A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). E-mail: winder@cbpf.br; Helayel Neto, J.A. [Universidade Catolica de Petropolis, RJ (Brazil). Grupo de Fisica Teorica. E-mail: helayel@cbpf.br
2000-05-01
Classical Maxwell and Maxwell-Chern-Simons Electrodynamics in (2+1) D are studied in some details. General expressions for the potential and fields are obtained for both models, and some particular cases are explicitly solved. Conceptual and technical difficulties arise, however, for accelerated charges. The propagation of electromagnetic signals is also studied and their reverberation is worked out and discussed. Furthermore, we show that a Dirac-like monopole yields a (static) tangential electric field. We also discuss some classical and quantum consequences of the field created by such a monopole when acting upon an usual electric charge. In particular, we show that at large distances, the dynamics of one single charged particle under the action of such a potential and a constant (external) magnetic field as well, reduces to that of one central harmonic oscillator, presenting, however, an interesting angular sector which admits energy-eigenvalues. For example, the quantisation of these eigenvalues yields a Dirac-like condition on the product of the charges. Moreover, such eigenvalues are shown to feel (and respond) to discrete shift of the angle variable. We also raise the question on the possibility of the formation pf bound states in this system. (author)
Geometric symmetries and topological terms in F-theory and field theory
Energy Technology Data Exchange (ETDEWEB)
Kapfer, Andreas
2016-08-25
In this thesis we investigate topological aspects and arithmetic structures in quantum field theory and string theory. Particular focus is put on consistent truncations of supergravity and compactifications of F-theory. The first part treats settings of supersymmetry breaking in five dimensions. We focus on an N=4 to N=2 breaking in gauged supergravity. For certain classes of embedding tensors we can analyze the theory around the vacuum to a great extent. Importantly, one-loop corrections to Chern-Simons terms are generically induced which are independent of the supersymmetry-breaking scale. We investigate concrete examples of consistent truncations of supergravity and M-theory which show this N=4 to N=2 breaking pattern in five dimensions. In particular, we analyze necessary conditions for these consistent truncations to be used as effective theories for phenomenology by demanding consistency of the scale-independent corrections to Chern-Simons couplings. The second part is devoted to the study of anomalies and large gauge transformations in circle-reduced gauge theories and F-theory. We consider four- and six-dimensional matter-coupled gauge theories on the circle and classify all large gauge transformations that preserve the boundary conditions of the matter fields. Enforcing that they act consistently on one-loop Chern-Simons couplings in three and five dimensions explicitly yields all higher-dimensional gauge anomaly cancelation conditions. In the context of F-theory compactifications we identify the classified large gauge transformations along the circle with arithmetic structures on elliptically fibered Calabi-Yau manifolds via the dual M-theory setting. Integer Abelian large gauge transformations correspond to free basis shifts in the Mordell-Weil lattice of rational sections while special fractional non-Abelian large gauge transformations are matched to torsional shifts in the Mordell-Weil group. For integer non-Abelian large gauge transformations we
Quantum field theory and link invariants
International Nuclear Information System (INIS)
Cotta-Ramusino, P.; Guadagnini, E.; Mintchev, M.; Martellini, M.
1990-01-01
A skein relation for the expectation values of Wilson line operators in three-dimensional SU(N) Chern-Simons gauge theory is derived at first order in the coupling constant. We use a variational method based on the properties of the three-dimensional field theory. The relationship between the above expectation values and the known link invariants is established. (orig.)
Topics in low-dimensional field theory
International Nuclear Information System (INIS)
Crescimanno, M.J.
1991-01-01
Conformal field theory is a natural tool for understanding two- dimensional critical systems. This work presents results in the lagrangian approach to conformal field theory. The first sections are chiefly about a particular class of field theories called coset constructions and the last part is an exposition of the connection between two-dimensional conformal theory and a three-dimensional gauge theory whose lagrangian is the Chern-Simons density
SO(N) reformulated link invariants from topological strings
International Nuclear Information System (INIS)
Borhade, Pravina; Ramadevi, P.
2005-01-01
Large N duality conjecture between U(N) Chern-Simons gauge theory on S 3 and A-model topological string theory on the resolved conifold was verified at the level of partition function and Wilson loop observables. As a consequence, the conjectured form for the expectation value of the topological operators in A-model string theory led to a reformulation of link invariants in U(N) Chern-Simons theory giving new polynomial invariants whose integer coefficients could be given a topological meaning. We show that the A-model topological operator involving SO(N) holonomy leads to a reformulation of link invariants in SO(N) Chern-Simons theory. Surprisingly, the SO(N) reformulated invariants also has a similar form with integer coefficients. The topological meaning of the integer coefficients needs to be explored from the duality conjecture relating SO(N) Chern-Simons theory to A-model closed string theory on orientifold of the resolved conifold background
Gauge theories of infinite dimensional Hamiltonian superalgebras
International Nuclear Information System (INIS)
Sezgin, E.
1989-05-01
Symplectic diffeomorphisms of a class of supermanifolds and the associated infinite dimensional Hamiltonian superalgebras, H(2M,N) are discussed. Applications to strings, membranes and higher spin field theories are considered: The embedding of the Ramond superconformal algebra in H(2,1) is obtained. The Chern-Simons gauge theory of symplectic super-diffeomorphisms is constructed. (author). 29 refs
Classical gauge theories on the coadjoint orbits of infinite dimensional groups
International Nuclear Information System (INIS)
Grabowski, M.P.; Virginia Polytechnic Inst. and State Univ., Blacksburg; Tze Chiahsiung
1991-01-01
We reformulate several classical gauge theories on the coadjoint orbits of the semidirect product of the gauge group and the Weyl group. The construction is given for the Yang-Mills theories in arbitrary spacetime dimension d, Chern-Simons topological theory (d=3) and higher dimensional topological models of Horowitz (d≥4). (orig.)
Energy Technology Data Exchange (ETDEWEB)
Pei, Du; Ye, Ke [Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA, 91125 (United States)
2016-11-02
We test the 3d-3d correspondence for theories that are labeled by Lens spaces. We find a full agreement between the index of the 3d N=2 “Lens space theory” T[L(p,1)] and the partition function of complex Chern-Simons theory on L(p,1). In particular, for p=1, we show how the familiar S{sup 3} partition function of Chern-Simons theory arises from the index of a free theory. For large p, we find that the index of T[L(p,1)] becomes a constant independent of p. In addition, we study T[L(p,1)] on the squashed three-sphere S{sub b}{sup 3}. This enables us to see clearly, at the level of partition function, to what extent G{sub ℂ} complex Chern-Simons theory can be thought of as two copies of Chern-Simons theory with compact gauge group G.
Research program in elementary particle theory
International Nuclear Information System (INIS)
1989-01-01
The Syracuse High Energy Theory group has continued to make significant contributions to many areas. Many novel aspects of Chern-Simons terms and effective Lagrangians were investigated. Various interesting aspects of quantum gravity and string theory were explored. Gauge models of elementary particles were studied in depth. The investigations of QCD at finite temperatures and multiply connected configuration spaces continued. 24 refs
Topological Field Theory of Time-Reversal Invariant Insulators
Energy Technology Data Exchange (ETDEWEB)
Qi, Xiao-Liang; Hughes, Taylor; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
We show that the fundamental time reversal invariant (TRI) insulator exists in 4 + 1 dimensions, where the effective field theory is described by the 4 + 1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2 + 1 dimensions. The TRI quantum spin Hall insulator in 2 + 1 dimensions and the topological insulator in 3 + 1 dimension can be obtained as descendants from the fundamental TRI insulator in 4 + 1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the Z{sub 2} topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant {alpha} = e{sup 2}/hc. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.
Equivariant Verlinde Formula from Fivebranes and Vortices
Gukov, Sergei; Pei, Du
2017-10-01
We study complex Chern-Simons theory on a Seifert manifold M 3 by embedding it into string theory. We show that complex Chern-Simons theory on M 3 is equivalent to a topologically twisted supersymmetric theory and its partition function can be naturally regularized by turning on a mass parameter. We find that the dimensional reduction of this theory to 2d gives the low energy dynamics of vortices in four-dimensional gauge theory, the fact apparently overlooked in the vortex literature. We also generalize the relations between (1) the Verlinde algebra, (2) quantum cohomology of the Grassmannian, (3) Chern-Simons theory on {Σ× S^1} and (4) index of a spin c Dirac operator on the moduli space of flat connections to a new set of relations between (1) the "equivariant Verlinde algebra" for a complex group, (2) the equivariant quantum K-theory of the vortex moduli space, (3) complex Chern-Simons theory on {Σ × S^1} and (4) the equivariant index of a spin c Dirac operator on the moduli space of Higgs bundles.
Exact Path Integral for 3D Quantum Gravity.
Iizuka, Norihiro; Tanaka, Akinori; Terashima, Seiji
2015-10-16
Three-dimensional Euclidean pure gravity with a negative cosmological constant can be formulated in terms of the Chern-Simons theory, classically. This theory can be written in a supersymmetric way by introducing auxiliary gauginos and scalars. We calculate the exact partition function of this Chern-Simons theory by using the localization technique. Thus, we obtain the quantum gravity partition function, assuming that it can be obtained nonperturbatively by summing over partition functions of the Chern-Simons theory on topologically different manifolds. The resultant partition function is modular invariant, and, in the case in which the central charge is expected to be 24, it is the J function, predicted by Witten.
Perfect Fluid Theory and its Extensions
Jackiw, R.; Nair, V. P.; Pi, S. -Y.; Polychronakos, A. P.
2004-01-01
We review the canonical theory for perfect fluids, in Eulerian and Lagrangian formulations. The theory is related to a description of extended structures in higher dimensions. Internal symmetry and supersymmetry degrees of freedom are incorporated. Additional miscellaneous subjects that are covered include physical topics concerning quantization, as well as mathematical issues of volume preserving diffeomorphisms and representations of Chern-Simons terms (= vortex or magnetic helicity).
Resonance – Journal of Science Education | Indian Academy of ...
Indian Academy of Sciences (India)
... 10; Issue 4. Of Connections and Fields – I-Chern's Mathematical Ideas in Physics ... Connection; curvature; magnetic monopoles; fibre bundles; gauge group; geometric phose; Chern-Weil theory; Chern-Simons theory. ... Current Issue : Vol.
Abelian tensor hierarchy in 4D, N=1 superspace
International Nuclear Information System (INIS)
Becker, Katrin; Becker, Melanie; III, William D. Linch; Robbins, Daniel
2016-01-01
With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in four-dimensional, N=1 superspace and construct its Chern-Simons-like invariants. When specialized to the case in which the tensors arise from a higher-dimensional theory, the invariants may be interpreted as higher-dimensional Chern-Simons forms reduced to four dimensions. As an application of the formalism, we construct the eleven-dimensional Chern-Simons form in terms of four-dimensional, N=1 superfields.
Abelian tensor hierarchy in 4D, N=1 superspace
Energy Technology Data Exchange (ETDEWEB)
Becker, Katrin; Becker, Melanie; III, William D. Linch; Robbins, Daniel [George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University, College Station, TX 77843 (United States)
2016-03-09
With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in four-dimensional, N=1 superspace and construct its Chern-Simons-like invariants. When specialized to the case in which the tensors arise from a higher-dimensional theory, the invariants may be interpreted as higher-dimensional Chern-Simons forms reduced to four dimensions. As an application of the formalism, we construct the eleven-dimensional Chern-Simons form in terms of four-dimensional, N=1 superfields.
A novel supersymmetry in 2-dimensional Yang-Mills theory on Riemann surfaces
International Nuclear Information System (INIS)
Soda, Jiro
1991-02-01
We find a novel supersymmetry in 2-dimensional Maxwell and Yang-Mills theories. Using this supersymmetry, it is shown that the 2-dimensional Euclidean pure gauge theory on a closed Riemann surface Σ can be reduced to a topological field theory which is the 3-dimensional Chern-Simons gauge theory in the special space-time topology Σ x R. Related problems are also discussed. (author)
Euler–Chern–Simons gravity from Lovelock–Born–Infeld gravity
Izaurieta, F.; Rodriguez, E.; Salgado, P.
2004-01-01
In the context of a gauge theoretical formulation, higher dimensional gravity invariant under the AdS group is dimensionally reduced to Euler-Chern-Simons gravity. The dimensional reduction procedure of Grignani-Nardelli [Phys. Lett. B 300, 38 (1993)] is generalized so as to permit reducing D-dimensional Lanczos Lovelock gravity to d=D-1 dimensions.
A geometric view on topologically massive gauge theories
International Nuclear Information System (INIS)
Horvathy, P.A.; Nash, C.
1985-01-01
The topologically massive gauge theory of Deser, Jackiw and Templeton is understood from Souriau's Principle of General Covariance. The non-gauge invariant mass term corresponds to a non-trivial class in the first cohomology group of configuration space, generated by the Chern-Simons secondary characteristic class. Quantization requires this class to be integral
Polynomial invariants for torus knots and topological strings
International Nuclear Information System (INIS)
Labastida, J.M.F.
2001-01-01
We make a precision test of a recently proposed conjecture relating Chern-Simons gauge theory to topological string theory on the resolution of the conifold. First, we develop a systematic procedure to extract string amplitudes from vacuum expectation values (vevs) of Wilson loops in Chern-Simons gauge theory, and then we evaluate these vevs in arbitrary irreducible representations of SU(N) for torus knots. We find complete agreement with the predictions derived from the target space interpretation of the string amplitudes. We also show that the structure of the free energy of topological open string theory gives further constraints on the Chern-Simons vevs. Our work provides strong evidence towards an interpretation of knot polynomial invariants as generating functions associated to enumerative problems. (orig.)
Mohammed, Asadig; Murugan, Jeff; Nastase, Horatiu
2012-11-02
We present an embedding of the three-dimensional relativistic Landau-Ginzburg model for condensed matter systems in an N = 6, U(N) × U(N) Chern-Simons-matter theory [the Aharony-Bergman-Jafferis-Maldacena model] by consistently truncating the latter to an Abelian effective field theory encoding the collective dynamics of O(N) of the O(N(2)) modes. In fact, depending on the vacuum expectation value on one of the Aharony-Bergman-Jafferis-Maldacena scalars, a mass deformation parameter μ and the Chern-Simons level number k, our Abelianization prescription allows us to interpolate between the Abelian Higgs model with its usual multivortex solutions and a Ø(4) theory. We sketch a simple condensed matter model that reproduces all the salient features of the Abelianization. In this context, the Abelianization can be interpreted as giving a dimensional reduction from four dimensions.
International Nuclear Information System (INIS)
Huang Yongchang; Huo Qiuhong
2008-01-01
Using Faddeev-Senjanovic path integral quantization for constrained Hamilton system, we quantize SU(n) N=2 supersymmetric gauge field system with non-Abelian Chern-Simons topological term in 2+1 dimensions. We use consistency of Coulomb gauge condition to naturally deduce a new gauge condition. Furthermore, we obtain the generating functional of Green function in phase space, deduce the angular momentum based on the global canonical Noether theorem at quantum level, obtain the fractional spin of this supersymmetric system, and show that the total angular momentum is the sum of the orbital angular momentum and spin angular momentum of the non-Abelian gauge field. Finally, we obtain the anomalous fractional spin and discover that the fractional spin has the contributions of both the group superscript components and A 0 s (x) charge
Research program in elementary particle theory
International Nuclear Information System (INIS)
Balachandran, A.P.; Rosenzweig, C.; Schechter, J.; Wali, K.C.
1992-01-01
In this paper we give a brief account of the work of the group during the past year. The topics covered here include (1) Effective Lagrangians and Solitons; (2) Chern-Simons and Conformal Field Theories; (3) Spin and Statistics; (4) The Standard Model and Beyond; (5) Non-Abelian Monopoles; (6) The Inflationary Universe; (7) The Hubbard Model, and (8) Miscellaneous
Moving vortices in noncommutative gauge theory
International Nuclear Information System (INIS)
Horvathy, P.A.; Stichel, P.C.
2004-01-01
Exact time-dependent solutions of nonrelativistic noncommutative Chern-Simons gauge theory are presented in closed analytic form. They are different from (indeed orthogonal to) those discussed recently by Hadasz, Lindstroem, Rocek and von Unge. Unlike theirs, our solutions can move with an arbitrary constant velocity, and can be obtained from the previously known static solutions by the recently found 'exotic' boost symmetry
Super-Galilei invariant field theories in 2+1 dimensions
International Nuclear Information System (INIS)
Bergman, O.; Thorn, C.B.
1995-01-01
The authors extend the Galilei group of space-time transformations by gradation, construct interacting field-theoretic representations of this algebra, and show that non-relativistic Super-Chern-Simons theory is a special case. They also study the generalization to matrix valued fields, which are relevant to the formulation of superstring theory as a 1/N c expansion of a field theory. The authors find that in the matrix case, the field theory is much more restricted by the supersymmetry
On the infinite-dimensional spin-2 symmetries in Kaluza-Klein theories
International Nuclear Information System (INIS)
Hohm, O.; Hamburg Univ.
2005-11-01
We consider the couplings of an infinite number of spin-2 fields to gravity appearing in Kaluza-Klein theories. They are constructed as the broken phase of a massless theory possessing an infinite-dimensional spin-2 symmetry. Focusing on a circle compactification of four-dimensional gravity we show that the resulting gravity/spin-2 system in D=3 has in its unbroken phase an interpretation as a Chern-Simons theory of the Kac-Moody algebra iso(1,2) associated to the Poincare group and also fits into the geometrical framework of algebra-valued differential geometry developed by Wald. Assigning all degrees of freedom to scalar fields, the matter couplings in the unbroken phase are determined, and it is shown that their global symmetry algebra contains the Virasoro algebra together with an enhancement of the Ehlers group SL(2,R) to its affine extension. The broken phase is then constructed by gauging a subgroup of the global symmetries. It is shown that metric, spin-2 fields and Kaluza-Klein vectors combine into a Chern-Simons theory for an extended algebra, in which the affine Poincare subalgebra acquires a central extension. (orig.)
Gauge theories of Yang-Mills vector fields coupled to antisymmetric tensor fields
International Nuclear Information System (INIS)
Anco, Stephen C.
2003-01-01
A non-Abelian class of massless/massive nonlinear gauge theories of Yang-Mills vector potentials coupled to Freedman-Townsend antisymmetric tensor potentials is constructed in four space-time dimensions. These theories involve an extended Freedman-Townsend-type coupling between the vector and tensor fields, and a Chern-Simons mass term with the addition of a Higgs-type coupling of the tensor fields to the vector fields in the massive case. Geometrical, field theoretic, and algebraic aspects of the theories are discussed in detail. In particular, the geometrical structure mixes and unifies features of Yang-Mills theory and Freedman-Townsend theory formulated in terms of Lie algebra valued curvatures and connections associated to the fields and nonlinear field strengths. The theories arise from a general determination of all possible geometrical nonlinear deformations of linear Abelian gauge theory for one-form fields and two-form fields with an Abelian Chern-Simons mass term in four dimensions. For this type of deformation (with typical assumptions on the allowed form considered for terms in the gauge symmetries and field equations), an explicit classification of deformation terms at first-order is obtained, and uniqueness of deformation terms at all higher orders is proven. This leads to a uniqueness result for the non-Abelian class of theories constructed here
Symmetry analysis for anisotropic field theories
International Nuclear Information System (INIS)
Parra, Lorena; Vergara, J. David
2012-01-01
The purpose of this paper is to study with the help of Noether's theorem the symmetries of anisotropic actions for arbitrary fields which generally depend on higher order spatial derivatives, and to find the corresponding current densities and the Noether charges. We study in particular scale invariance and consider the cases of higher derivative extensions of the scalar field, electrodynamics and Chern-Simons theory.
Computing black hole entropy in loop quantum gravity from a conformal field theory perspective
International Nuclear Information System (INIS)
Agulló, Iván; Borja, Enrique F.; Díaz-Polo, Jacobo
2009-01-01
Motivated by the analogy proposed by Witten between Chern-Simons and conformal field theories, we explore an alternative way of computing the entropy of a black hole starting from the isolated horizon framework in loop quantum gravity. The consistency of the result opens a window for the interplay between conformal field theory and the description of black holes in loop quantum gravity
Inoenue-Wigner contraction and D = 2 + 1 supergravity
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Concha, P.K.; Rodriguez, E.K. [Universidad Adolfo Ibanez, Departamento de Ciencias, Facultad de Artes Liberales, Vina del Mar (Chile); Universidad Austral de Chile, Instituto de Ciencias Fisicas y Matematicas, Valdivia (Chile); Fierro, O. [Universidad Catolica de la Santisima Concepcion, Departamento de Matematica y Fisica Aplicadas, Concepcion (Chile)
2017-01-15
We present a generalization of the standard Inoenue-Wigner contraction by rescaling not only the generators of a Lie superalgebra but also the arbitrary constants appearing in the components of the invariant tensor. The procedure presented here allows one to obtain explicitly the Chern-Simons supergravity action of a contracted superalgebra. In particular we show that the Poincare limit can be performed to a D = 2 + 1 (p,q) AdS Chern-Simons supergravity in presence of the exotic form. We also construct a new three-dimensional (2,0) Maxwell Chern-Simons supergravity theory as a particular limit of (2,0) AdS-Lorentz supergravity theory. The generalization for N = p + q gravitinos is also considered. (orig.)
A Kallosh theorem for BF-type topological field theory
International Nuclear Information System (INIS)
Birmingham, D.; Gibbs, R.; Mokhtari, S.
1991-01-01
A Kallosh theorem is established for the case of BF-type theories in three dimensions, including a coupling to Chern-Simons theory. The phase contribution to the one-loop off-shell effective action is computed for a two-parameter family of local covariant gauges. It is shown that the phase is independent of these parameters, and thus equals the 'no Vilkovisky-DeWitt' gauge result. The field space metric dependence of a corresponding calculation for generalized BF theory is briefly discussed. (orig.)
Differential and integral forms in supergauge theories and supergravity
International Nuclear Information System (INIS)
Zupnik, B.M.; Pak, D.G.
1989-01-01
D = 3, 4, N = 1 supergauge theories and D = 3, N = 1 supergravity are considered in the superfield formalism by using differential and integral forms. A special map of the space of differential forms into the space of integral forms is proposed. By means of this map we find the superfield Chern-Simons terms in D = 3, N = 1 Yang-Mills theory and supergravity. The integral forms corresponding to superfield invariants of D = 4, N = 1 supergauge theory have also been constructed. (Author)
International Nuclear Information System (INIS)
Tze, Chia-Hsiung
1989-01-01
By way of the Gauss-Bonnet-Chern theorem, we present a higher dimensional extension of Polyakov's regularization of Wilson loops of point solitons. Spacetime paths of extended objects become hyper-ribbons with self-linking, twisting and writhing numbers. specifically we discuss the exotic spin and statistical phase entanglements of geometric n-membrane solitons of D-dimensional KP 1 σ-models with an added Hopf-Chern-Simons term where (n, D, K) = (0, 3, C), (2, 7, H), (6, 15, Ω). They are uniquely linked to the complex and quaternion and octonion division algebras. 22 refs
On the energy crisis in noncommutative CP(1) model
International Nuclear Information System (INIS)
Sourrouille, Lucas
2010-01-01
We study the CP(1) system in (2+1)-dimensional noncommutative space with and without Chern-Simons term. Using the Seiberg-Witten map we convert the noncommutative CP(1) system to an action written in terms of the commutative fields. We find that this system presents the same infinite size instanton solution as the commutative Chern-Simons-CP(1) model without a potential term. Based on this result we argue that the BPS equations are compatible with the full variational equations of motion, rejecting the hypothesis of an 'energy crisis'. In addition we examine the noncommutative CP(1) system with a Chern-Simons interaction. In this case we find that when the theory is transformed by the Seiberg-Witten map it also presents the same instanton solution as the commutative Chern-Simons-CP(1) model.
Theory of orbital magnetoelectric response
International Nuclear Information System (INIS)
Malashevich, Andrei; Souza, Ivo; Coh, Sinisa; Vanderbilt, David
2010-01-01
We extend the recently developed theory of bulk orbital magnetization to finite electric fields, and use it to calculate the orbital magnetoelectric (ME) response of periodic insulators. Working in the independent-particle framework, we find that the finite-field orbital magnetization can be written as a sum of three gauge-invariant contributions, one of which has no counterpart at zero field. The extra contribution is collinear with and explicitly dependent on the electric field. The expression for the orbital magnetization is suitable for first-principles implementations, allowing one to calculate the ME response coefficients by numerical differentiation. Alternatively, perturbation-theory techniques may be used, and for that purpose we derive an expression directly for the linear ME tensor by taking the first field-derivative analytically. Two types of terms are obtained. One, the 'Chern-Simons' term, depends only on the unperturbed occupied orbitals and is purely isotropic. The other, 'Kubo' terms, involve the first-order change in the orbitals and give isotropic as well as anisotropic contributions to the response. In ordinary ME insulators all terms are generally present, while in strong Z 2 topological insulators only the Chern-Simons term is allowed, and is quantized. In order to validate the theory, we have calculated under periodic boundary conditions the linear ME susceptibility for a 3D tight-binding model of an ordinary ME insulator, using both the finite-field and perturbation-theory expressions. The results are in excellent agreement with calculations on bounded samples.
Quantum field theory in 2+1 dimensions
International Nuclear Information System (INIS)
Marino, E.C.
1998-01-01
An introductory review is made of many outstanding features of Quantum Field Theory formulated in three-dimensional spacetime. These include topological properties, the Huygens Principle, the Coulomb potential, topological excitations like vortices and skyrmions, dynamical mass generation, fractional spin and statistics, duality nd bosonization. Theories including the Maxwell-Chern-Simons, Abelian Higgs and C P 1 -Nonlinear Sigma Model are used to illustrate the different features. Applications to High-T c Superconductivity and to the Quantum Hall Effect are also presented. (author)
Stress tensor correlators of CCFT{sub 2} using flat-space holography
Energy Technology Data Exchange (ETDEWEB)
Asadi, Mohammad; Baghchesaraei, Omid; Fareghbal, Reza [Shahid Beheshti University, Department of Physics, Tehran (Iran, Islamic Republic of)
2017-11-15
We use the correspondence between three-dimensional asymptotically flat spacetimes and two-dimensional contracted conformal field theories (CCFTs) to derive the stress tensor correlators of CCFT{sub 2}. On the gravity side we use the metric formulation instead of the Chern-Simons formulation of three-dimensional gravity. This method can also be used for the four-dimensional case, where there is no Chern-Simons formulation for the bulk theory. (orig.)
A Kallosh theorem for BF-type topological field theory
Energy Technology Data Exchange (ETDEWEB)
Birmingham, D. (Theory Div., CERN, Geneva (Switzerland)); Gibbs, R.; Mokhtari, S. (Physics Dept., Louisiana Tech. Univ., Ruston, LA (United States))
1991-12-12
A Kallosh theorem is established for the case of BF-type theories in three dimensions, including a coupling to Chern-Simons theory. The phase contribution to the one-loop off-shell effective action is computed for a two-parameter family of local covariant gauges. It is shown that the phase is independent of these parameters, and thus equals the 'no Vilkovisky-DeWitt' gauge result. The field space metric dependence of a corresponding calculation for generalized BF theory is briefly discussed. (orig.).
An introduction to topological Yang-Mills theory
International Nuclear Information System (INIS)
Baal, P. van; Rijksuniversiteit Utrecht
1990-01-01
In these lecture notes I give a ''historical'' introduction to topological gauge theories. My main aim is to clearly explain the origin of the Hamiltonian which forms the basis of Witten's construction of topological gauge theory. I show how this Hamiltonian arises from Witten's formulation of Morse theory as applied by Floer to the infinite dimensional space of gauge connections, with the Chern-Simons functional as the appriopriate Morse function(al). I therefore discuss the De Rham cohomology, Hodge theory, Morse theory, Floer homology, Witten's construction of the Lagrangian for topological gauge theory, the subsequent BRST formulation of topological quantum field theory and finally Witten's construction of the Donaldson polynomials. (author)
Spin Singlet Quantum Hall Effect and nonabelian Landau-Ginzburg theory
International Nuclear Information System (INIS)
Balatsky, A.
1991-01-01
In this paper we present a theory of Singlet Quantum Hall Effect (SQHE). We show that the Halperin-Haldane SQHE wave function can be written in the form of a product of a wave function for charged semions in a magnetic field and a wave function for the Chiral Spin Liquid of neutral spin-1/2 semions. We introduce field-theoretic model in which the electron operators are factorized in terms of charged spinless semions (holons) and neutral spin-1/2 semions (spinons). Broken time reversal symmetry and short ranged spin correlations lead to Su(2) κ=1 Chern-Simons term in Landau-Ginzburg action for SQHE phase. We construct appropriate coherent states for SQHE phase and show the existence of SU(2) valued gauge potential. This potential appears as a result of ''spin rigidity'' of the ground state against any displacements of nodes of wave function from positions of the particles and reflects the nontrivial monodromy in the presence of these displacenmants. We argue that topological structure of Su(2) κ=1 Chern-Simons theory unambiguously dictates semion statistics of spinons. 19 refs
On the duality in CPT-even Lorentz-breaking theories
Energy Technology Data Exchange (ETDEWEB)
Scarpelli, A.P.B. [Departamento de Policia Federal, Sao Paulo (Brazil); Ribeiro, R.F.; Nascimento, J.R.; Petrov, A.Yu. [Universidade Federal da Paraiba, Departamento de Fisica (Brazil)
2015-07-15
We generalize the duality between self-dual and Maxwell-Chern-Simons theories for the case of a CPT-even Lorentz-breaking extension of these theories. The duality is shown using the gauge embedding procedure, both in free and coupled cases, and with the master action approach. The physical spectra of both Lorentz-breaking theories are studied. The massive poles are shown to coincide and to respect the requirements for unitarity and causality at tree level. The extra massless poles which are present in the dualized model are shown to be nondynamical. (orig.)
On the duality in CPT-even Lorentz-breaking theories
International Nuclear Information System (INIS)
Scarpelli, A.P.B.; Ribeiro, R.F.; Nascimento, J.R.; Petrov, A.Yu.
2015-01-01
We generalize the duality between self-dual and Maxwell-Chern-Simons theories for the case of a CPT-even Lorentz-breaking extension of these theories. The duality is shown using the gauge embedding procedure, both in free and coupled cases, and with the master action approach. The physical spectra of both Lorentz-breaking theories are studied. The massive poles are shown to coincide and to respect the requirements for unitarity and causality at tree level. The extra massless poles which are present in the dualized model are shown to be nondynamical. (orig.)
Renormalization of topological field theory
International Nuclear Information System (INIS)
Birmingham, D.; Rakowski, M.; Thompson, G.
1988-11-01
One loop corrections to topological field theory in three and four dimensions are presented. By regularizing determinants, we compute the effective action and β-function in four dimensional topological Yang-Mills theory and find that the BRST symmetry is preserved. Moreover, the minima of the effective action still correspond to instanton configurations. In three dimensions, an analysis of the Chern-Simons theory shows that the topological nature of the theory is also preserved to this order. In addition, we find that this theory possesses an extra supersymmetry when quantized in the Landau gauge. Using dimensional regularization, we then study the Ward identities of the extended BRST symmetry in the three dimensional topological Yang-Mills-Higgs model. (author). 22 refs
Superconformal quantum field theories in string. Gauge theory dualities
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Wiegandt, Konstantin
2012-08-14
In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investigated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop/amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.
Superconformal quantum field theories in string. Gauge theory dualities
International Nuclear Information System (INIS)
Wiegandt, Konstantin
2012-01-01
In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investigated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop/amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.
Euclidean D-branes and higher-dimensional gauge theory
International Nuclear Information System (INIS)
Acharya, B.S.; Figueroa-O'Farrill, J.M.; Spence, B.; O'Loughlin, M.
1997-07-01
We consider euclidean D-branes wrapping around manifolds of exceptional holonomy in dimensions seven and eight. The resulting theory on the D-brane-that is, the dimensional reduction of 10-dimensional supersymmetric Yang-Mills theory-is a cohomological field theory which describes the topology of the moduli space of instantons. The 7-dimensional theory is an N T =2 (or balanced) cohomological theory given by an action potential of Chern-Simons type. As a by-product of this method, we construct a related cohomological field theory which describes the monopole moduli space on a 7-manifold of G 2 holonomy. (author). 22 refs, 3 tabs
Two field formulation of closed string field theory
International Nuclear Information System (INIS)
Bogojevic, A.R.
1990-09-01
A formulation of closed string field theory is presented that is based on a two field action. It represents a generalization of Witten's Chern-Simons formulation of 3d gravity. The action contains only 3 string interactions and no string field truncations, unlike the previous non-polynomial action of Zwiebach. The two field action is found to follow from a purely cubic, background independent action similar to the one for open strings. (orig.)
Topological BF field theory description of topological insulators
International Nuclear Information System (INIS)
Cho, Gil Young; Moore, Joel E.
2011-01-01
Research highlights: → We show that a BF theory is the effective theory of 2D and 3D topological insulators. → The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. → The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. → Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a π flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.
Universal character and large N factorization in topological gauge/string theory
International Nuclear Information System (INIS)
Kanno, Hiroaki
2006-01-01
We establish a formula of the large N factorization of the modular S-matrix for the coupled representations in U(N) Chern-Simons theory. The formula was proposed by Aganagic, Neitzke and Vafa, based on computations involving the conifold transition. We present a more rigorous proof that relies on the universal character for rational representations and an expression of the modular S-matrix in terms of the specialization of characters
A general solution of the BV-master equation and BRST field theories
International Nuclear Information System (INIS)
Dayi, O.F.
1993-05-01
For a class of first order gauge theories it was shown that the proper solution of the BV-master equation can be obtained straightforwardly. Here we present the general condition which the gauge generators should satisfy to conclude that this construction is relevant. The general procedure is illustrated by its application to the Chern-Simons theory in any odd-dimension. Moreover, it is shown that this formalism is also applicable to BRST field theories, when one replaces the role of the exterior derivative with the BRST charge of first quantization. (author). 17 refs
Supergravity and Yang-Mills theories as generalized topological fields with constraints
International Nuclear Information System (INIS)
Ling Yi; Tung Rohsuan; Guo Hanying
2004-01-01
We present a general approach to construct a class of generalized topological field theories with constraints by means of generalized differential calculus and its application to connection theory. It turns out that not only the ordinary BF formulations of general relativity and Yang-Mills theories, but also the N=1,2 chiral supergravities can be reformulated as these constrained generalized topological field theories once the free parameters in the Lagrangian are specially chosen. We also show that the Chern-Simons action on the boundary may naturally be induced from the generalized topological action in the bulk, rather than introduced by hand
Effective field theory and integrability in two-dimensional Mott transition
International Nuclear Information System (INIS)
Bottesi, Federico L.; Zemba, Guillermo R.
2011-01-01
Highlights: → Mott transition in 2d lattice fermion model. → 3D integrability out of 2D. → Effective field theory for Mott transition in 2d. → Double Chern-Simons. → d-Density waves. - Abstract: We study the Mott transition in a two-dimensional lattice spinless fermion model with nearest neighbors density-density interactions. By means of a two-dimensional Jordan-Wigner transformation, the model is mapped onto the lattice XXZ spin model, which is shown to possess a quantum group symmetry as a consequence of a recently found solution of the Zamolodchikov tetrahedron equation. A projection (from three to two space-time dimensions) property of the solution is used to identify the symmetry of the model at the Mott critical point as U q (sl(2)-circumflex)xU q (sl(2)-circumflex), with deformation parameter q = -1. Based on this result, the low-energy effective field theory for the model is obtained and shown to be a lattice double Chern-Simons theory with coupling constant k = 1 (with the standard normalization). By further employing the effective filed theory methods, we show that the Mott transition that arises is of topological nature, with vortices in an antiferromagnetic array and matter currents characterized by a d-density wave order parameter. We also analyze the behavior of the system upon weak coupling, and conclude that it undergoes a quantum gas-liquid transition which belongs to the Ising universality class.
International Nuclear Information System (INIS)
Ezawa, Motohiko
2014-01-01
The Chern number is a genuine topological number. On the other hand, a symmetry protected topological (SPT) charge is a topological number only when a symmetry exists. We propose a formula for the SPT charge as a derivative of the Chern number in terms of the Green function in such a way that it is valid and related to the associated Hall current even when the symmetry is broken. We estimate the amount of deviation from the quantized value as a function of the strength of the broken symmetry. We present two examples. First, we consider Dirac electrons with the spin–orbit coupling on honeycomb lattice, where the SPT charges are given by the spin-Chern, valley-Chern and spin-valley-Chern numbers. Though the spin-Chern charge is not quantized in the presence of the Rashba coupling, the deviation is estimated to be 10 −7 in the case of silicene, a silicon cousin of graphene. Second, we analyze the effect of the mirror-symmetry breaking of the mirror-Chern number in a thin-film of topological crystalline insulator.
International Nuclear Information System (INIS)
Mansouri, F.; Suranyi, P.; Wijewardhana, L.C.R.; Witten, L.
1990-10-01
A 2+1 dimensional deSitter Chern-Simons theory has been constructed and shown to be consistent. Wilson loop variables have been computed and shown to close under Poisson bracket operation for N = 2 Poincare supergravity. It has also been shown that there are two equivalent pictures of describing two particle scattering in 2+1 dimensional gravity theory, which are related by multivalued gauge transformations. We have generalized the Jackiw-Johnson sumrule, relating Goldstone boson decay constants to the dynamical masses of fermions, to an arbitrary symmetry group. We have analyzed dynamical parity breaking in 2+1 dimensional 4-fermi theories. Finally, we have found the partition function for a system of free parabosons and parafermions of order two. 53 refs
OSp(5|4) superconformal symmetry of N=5 Chern–Simons theory
International Nuclear Information System (INIS)
Chen, Fa-Min
2013-01-01
We demonstrate that the general D=3, N=5 Chern–Simons matter theory possesses a full OSp(5|4) superconformal symmetry, and construct the corresponding superconformal currents. The closure of the superconformal algebra is verified in detail. We also show that the conserved OSp(6|4) superconformal currents in the general N=6 theory can be obtained as special cases of the OSp(5|4) currents by enhancing the R-symmetry of the N=5 theory from USp(4) to SU(4)
Quaternion based generalization of Chern–Simons theories in arbitrary dimensions
Directory of Open Access Journals (Sweden)
Alessandro D'Adda
2017-08-01
Full Text Available A generalization of Chern–Simons gauge theory is formulated in any dimension and arbitrary gauge group where gauge fields and gauge parameters are differential forms of any degree. The quaternion algebra structure of this formulation is shown to be equivalent to a three Z2-gradings structure, thus clarifying the quaternion role in the previous formulation.
An off-shell formulation of N=4 supersymmetric Yang-Mills theory in twistor harmonic superspace
International Nuclear Information System (INIS)
Sokatchev, E.
1989-01-01
Twistor-like harmonic variables which parametrize the coset space SO(1, 4)/SO(1, 2)xSO(2) are introduced. With their help the on-shell constraints for N=4, d=5 supersymmetric Yang-Mills theory are rewritten as conditions for flatness in the harmonic directions of superspace. A Chern-Simons off-shell action leading to those equations is proposed. There are indications that the off-shell theory might be finite, despite the fact that the on-shell one seems non-renormalizable. (orig.)
On CSM classes via Chern-Fulton classes of f-schemes
Fullwood, James; Wang, Dongxu
2015-01-01
The Chern-Fulton class is a generalization of Chern class to the realm of arbitrary embeddable schemes. While Chern-Fulton classes are sensitive to non-reduced scheme structure, they are not sensitive to possible singularities of the underlying support, thus at first glance are not interesting from a singularity theory viewpoint. However, we introduce a class of formal objects which we think of as `fractional schemes', or f-schemes for short, and then show that when one broadens the domain of...
Dynamical generation of non-abelian gauge group via the improved perturbation theory
International Nuclear Information System (INIS)
Kuroki, Tsunehide
2008-01-01
It was suggested that the massive Yang-Mills-Chern-Simons matrix model has three phases and that in one of them a non-Abelian gauge symmetry is dynamically generated. The analysis was at the one-loop level around a classical solution of fuzzy sphere type. We obtain evidences that three phases are indeed realized as nonperturbative vacua by using the improved perturbation theory. It gives a good example that even if we start from a trivial vacuum, the improved perturbation theory around it enables us to observe nontrivial vacua. (author)
Fusion potentials for Gk and handle squashing
International Nuclear Information System (INIS)
Crescimanno, M.
1993-01-01
Using Chern-Simons gauge theory, we show that the fusion ring of the conformal field theory G k (G any Lie algebra) is isomorphic to P[u]/(∇V) where (∇V) is the ideal generated by conditions ∇V=0. We explicitly construct V for all G k . We also derive a residue-like formula for the correlation functions in the Chern-Simons theory thus providing an RCFT version of the residue formula for the topological Landau-Ginzburg model. An operator that acts like a measure in this residue formula has the interpretation of a handle-squashing operator and explicit formulae for this operator are given. (orig.)
Entanglement entropy and the colored Jones polynomial
Balasubramanian, Vijay; DeCross, Matthew; Fliss, Jackson; Kar, Arjun; Leigh, Robert G.; Parrikar, Onkar
2018-05-01
We study the multi-party entanglement structure of states in Chern-Simons theory created by performing the path integral on 3-manifolds with linked torus boundaries, called link complements. For gauge group SU(2), the wavefunctions of these states (in a particular basis) are the colored Jones polynomials of the corresponding links. We first review the case of U(1) Chern-Simons theory where these are stabilizer states, a fact we use to re-derive an explicit formula for the entanglement entropy across a general link bipartition. We then present the following results for SU(2) Chern-Simons theory: (i) The entanglement entropy for a bipartition of a link gives a lower bound on the genus of surfaces in the ambient S 3 separating the two sublinks. (ii) All torus links (namely, links which can be drawn on the surface of a torus) have a GHZ-like entanglement structure — i.e., partial traces leave a separable state. By contrast, through explicit computation, we test in many examples that hyperbolic links (namely, links whose complements admit hyperbolic structures) have W-like entanglement — i.e., partial traces leave a non-separable state. (iii) Finally, we consider hyperbolic links in the complexified SL(2,C) Chern-Simons theory, which is closely related to 3d Einstein gravity with a negative cosmological constant. In the limit of small Newton constant, we discuss how the entanglement structure is controlled by the Neumann-Zagier potential on the moduli space of hyperbolic structures on the link complement.
Bimetric Theory of Fractional Quantum Hall States
Gromov, Andrey; Son, Dam Thanh
2017-10-01
We present a bimetric low-energy effective theory of fractional quantum Hall (FQH) states that describes the topological properties and a gapped collective excitation, known as the Girvin-Macdonald-Platzman (GMP) mode. The theory consists of a topological Chern-Simons action, coupled to a symmetric rank-2 tensor, and an action à la bimetric gravity, describing the gapped dynamics of a spin-2 mode. The theory is formulated in curved ambient space and is spatially covariant, which allows us to restrict the form of the effective action and the values of phenomenological coefficients. Using bimetric theory, we calculate the projected static structure factor up to the k6 order in the momentum expansion. To provide further support for the theory, we derive the long-wave limit of the GMP algebra, the dispersion relation of the GMP mode, and the Hall viscosity of FQH states. The particle-hole (PH) transformation of the theory takes a very simple form, making the duality between FQH states and their PH conjugates manifest. We also comment on the possible applications to fractional Chern insulators, where closely related structures arise. It is shown that the familiar FQH observables acquire a curious geometric interpretation within the bimetric formalism.
Bimetric Theory of Fractional Quantum Hall States
Directory of Open Access Journals (Sweden)
Andrey Gromov
2017-11-01
Full Text Available We present a bimetric low-energy effective theory of fractional quantum Hall (FQH states that describes the topological properties and a gapped collective excitation, known as the Girvin-Macdonald-Platzman (GMP mode. The theory consists of a topological Chern-Simons action, coupled to a symmetric rank-2 tensor, and an action à la bimetric gravity, describing the gapped dynamics of a spin-2 mode. The theory is formulated in curved ambient space and is spatially covariant, which allows us to restrict the form of the effective action and the values of phenomenological coefficients. Using bimetric theory, we calculate the projected static structure factor up to the k^{6} order in the momentum expansion. To provide further support for the theory, we derive the long-wave limit of the GMP algebra, the dispersion relation of the GMP mode, and the Hall viscosity of FQH states. The particle-hole (PH transformation of the theory takes a very simple form, making the duality between FQH states and their PH conjugates manifest. We also comment on the possible applications to fractional Chern insulators, where closely related structures arise. It is shown that the familiar FQH observables acquire a curious geometric interpretation within the bimetric formalism.
Factorization algebras in quantum field theory
Costello, Kevin
2017-01-01
Factorization algebras are local-to-global objects that play a role in classical and quantum field theory which is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this first volume, the authors develop the theory of factorization algebras in depth, but with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern-Simons theory. Expositions of the relevant background in homological algebra, sheaves and functional analysis are also included, thus making this book ideal for researchers and graduates working at the interface between mathematics and physics.
The dual of the Carroll-Field-Jackiw model
International Nuclear Information System (INIS)
Guimaraes, M.S.; Grigorio, L.; Wotzasek, C.
2006-01-01
In this work we apply different duality techniques, both the dual projection, based on the soldering formalism and the master action, in order to obtain and study the dual description of the Carroll- Field-Jackiw model [1], a theory with a Chern-Simons-like explicitly Lorentz and CPT violating term, including the interaction with external charges. This Maxwell-Chern-Simons-like model may be rewritten in terms of the interacting modes of a massless scalar model and a topologically massive model [2], that are mapped, through duality, into interacting massless Maxwell and massive self-dual modes [3]. It is also shown that these dual modes might be represented into an unified rank-two self-dual model that represents the direct dual of the vector Maxwell-Chern-Simons-like model
Anomaly cancelation in field theory and F-theory on a circle
International Nuclear Information System (INIS)
Grimm, Thomas W.; Kapfer, Andreas
2016-01-01
We study the manifestation of local gauge anomalies of four- and six-dimensional field theories in the lower-dimensional Kaluza-Klein theory obtained after circle compactification. We identify a convenient set of transformations acting on the whole tower of massless and massive states and investigate their action on the low-energy effective theories in the Coulomb branch. The maps employ higher-dimensional large gauge transformations and precisely yield the anomaly cancelation conditions when acting on the one-loop induced Chern-Simons terms in the three- and five-dimensional effective theory. The arising symmetries are argued to play a key role in the study of the M-theory to F-theory limit on Calabi-Yau manifolds. For example, using the fact that all fully resolved F-theory geometries inducing multiple Abelian gauge groups or non-Abelian groups admit a certain set of symmetries, we are able to generally show the cancelation of pure Abelian or pure non-Abelian anomalies in these models.
Light-front quantization of field theory
Energy Technology Data Exchange (ETDEWEB)
Srivastava, Prem P. [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Inst. de Fisica]|[Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)
1996-07-01
Some basic topics in Light-Front (LF) quantized field theory are reviewed. Poincare algebra and the LF spin operator are discussed. The local scalar field theory of the conventional framework is shown to correspond to a non-local Hamiltonian theory on the LF in view of the constraint equations on the phase space, which relate the bosonic condensates to the non-zero modes. This new ingredient is useful to describe the spontaneous symmetry breaking on the LF. The instability of the symmetric phase in two dimensional scalar theory when the coupling constant grows is shown in the LF theory renormalized to one loop order. Chern-Simons gauge theory, regarded to describe excitations with fractional statistics, is quantized in the light-cone gauge and a simple LF Hamiltonian obtained which may allow us to construct renormalized theory of anyons. (author). 20 refs.
Light-front quantization of field theory
International Nuclear Information System (INIS)
Srivastava, Prem P.
1996-07-01
Some basic topics in Light-Front (LF) quantized field theory are reviewed. Poincare algebra and the LF spin operator are discussed. The local scalar field theory of the conventional framework is shown to correspond to a non-local Hamiltonian theory on the LF in view of the constraint equations on the phase space, which relate the bosonic condensates to the non-zero modes. This new ingredient is useful to describe the spontaneous symmetry breaking on the LF. The instability of the symmetric phase in two dimensional scalar theory when the coupling constant grows is shown in the LF theory renormalized to one loop order. Chern-Simons gauge theory, regarded to describe excitations with fractional statistics, is quantized in the light-cone gauge and a simple LF Hamiltonian obtained which may allow us to construct renormalized theory of anyons. (author). 20 refs
Solving topological field theories on mapping tori
International Nuclear Information System (INIS)
Blau, M.; Jermyn, I.; Thompson, G.
1996-05-01
Using gauge theory and functional integral methods, we derive concrete expressions for the partition functions of BF theory and the U(1 modul 1) model of Rozansky and Saleur on Σ x S 1 , both directly and using equivalent two-dimensional theories. We also derive the partition function on a certain non-abelian generalization of the U(1 modul 1) model on mapping tori and hence obtain explicit expressions for the Ray-Singer torsion on these manifolds. Extensions of these results to BF and Chern-Simons theories on mapping tori are also discussed. The topological field theory actions of the equivalent two- dimensional theories we find have the interesting property of depending explicitly on the diffeomorphism defining the mapping torus while the quantum field theory is sensitive only to its isomorphism class defining the mapping torus as a smooth manifold. (author). 20 refs
Quantization conditions and functional equations in ABJ(M) theories
International Nuclear Information System (INIS)
Grassi, Alba; Marino, Marcos; Hatsuda, Yasuyuki
2014-12-01
The partition function of ABJ(M) theories on the three-sphere can be regarded as the canonical partition function of an ideal Fermi gas with a non-trivial Hamiltonian. We propose an exact expression for the spectral determinant of this Hamiltonian, which generalizes recent results obtained in the maximally supersymmetric case. As a consequence, we find an exact WKB quantization condition determining the spectrum which is in agreement with numerical results. In addition, we investigate the factorization properties and functional equations for our conjectured spectral determinants. These functional equations relate the spectral determinants of ABJ theories with consecutive ranks of gauge groups but the same Chern-Simons coupling.
Non-planar ABJ theory and parity
International Nuclear Information System (INIS)
Caputa, Pawel; Kristjansen, Charlotte; Zoubos, Konstantinos
2009-01-01
While the ABJ Chern-Simons-matter theory and its string theory dual manifestly lack parity invariance, no sign of parity violation has so far been observed on the weak coupling spin chain side. In particular, the planar two-loop dilatation generator of ABJ theory is parity invariant. In this Letter we derive the non-planar part of the two-loop dilatation generator of ABJ theory in its SU(2)xSU(2) sub-sector. Applying the dilatation generator to short operators, we explicitly demonstrate that, for operators carrying excitations on both spin chains, the non-planar part breaks parity invariance. For operators with only one type of excitation, however, parity remains conserved at the non-planar level. We furthermore observe that, as for ABJM theory, the degeneracy between planar parity pairs is lifted when non-planar corrections are taken into account.
Non-planar ABJ Theory and Parity
DEFF Research Database (Denmark)
Caputa, Pawel; Kristjansen, Charlotte; Zoubos, Konstantinos
2009-01-01
we derive the non-planar part of the two-loop dilatation generator of ABJ theory in its SU(2)xSU(2) sub-sector. Applying the dilatation generator to short operators, we explicitly demonstrate that, for operators carrying excitations on both spin chains, the non-planar part breaks parity invariance......While the ABJ Chern-Simons-matter theory and its string theory dual manifestly lack parity invariance, no sign of parity violation has so far been observed on the weak coupling spin chain side. In particular, the planar two-loop dilatation generator of ABJ theory is parity invariant. In this letter....... For operators with only one type of excitation, however, parity remains conserved at the non-planar level. We furthermore observe that, as for ABJM theory, the degeneracy between planar parity pairs is lifted when non-planar corrections are taken into account....
Holographic currents in first order Gravity and finite Fefferman-Graham expansions
International Nuclear Information System (INIS)
Banados, Maximo; Miskovic, Olivera; Theisen, Stefan
2006-01-01
We study the holographic currents associated to Chern-Simons theories. We start with an example in three dimensions and find the holographic representations of vector and chiral currents reproducing the correct expression for the chiral anomaly. In five dimensions, Chern-Simons theory for AdS group describes first order gravity and we show that there exists a gauge fixing leading to a finite Fefferman-Graham expansion. We derive the corresponding holographic currents, namely, the stress tensor and spin current which couple to the metric and torsional degrees of freedom at the boundary, respectively. We obtain the correct Ward identities for these currents by looking at the bulk constraint equations
Chiral and parity anomalies at finite temperature and density
International Nuclear Information System (INIS)
Sisakyan, A.N.; Shevchenko, O.Yu.; Solganik, S.B.
1997-01-01
Two closely related topological phenomena are studied at finite density and temperature. These are chiral anomaly and Chern-Simons term. By using different methods it is shown that μ 2 =m 2 is the crucial point for Chern-Simons term at zero temperature. So when μ 2 2 , μ influence disappears and we get the usual Chern-Simons term. On the other hand, when μ 2 >m 2 , the Chern-Simons term vanishes because of nonzero density of background fermions. It occurs that the chiral anomaly doesn't depend on density and temperature. The connection between parity anomalous Chern-Simons term and chiral anomaly is generalized on finite density. These results hold in any dimension both in Abelian and in non-Abelian cases
A simple remark on three dimensional gauge theories
International Nuclear Information System (INIS)
Lemes, V.E.R.; Linhares de Jesus, C.; Sasaki, C.A.G.; Sorella, S.P.; Vilar, L.C.Q.; Ventura, O.S.
1997-08-01
Classical three dimensional Yang-Mills is seen to be related to the topological Chern-Simons term through a nonlinear but fully local and covariant gauge field redefinition. A classical recursive cohomological argument is proved. (author)
Energy Technology Data Exchange (ETDEWEB)
Alday, Luis F.; Genolini, Pietro Benetti; Bullimore, Mathew; Loon, Mark van [Mathematical Institute, University of Oxford, Andrew Wiles Building,Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG (United Kingdom)
2017-04-28
We explore aspects of the correspondence between Seifert 3-manifolds and 3d N=2 supersymmetric theories with a distinguished abelian flavour symmetry. We give a prescription for computing the squashed three-sphere partition functions of such 3d N=2 theories constructed from boundary conditions and interfaces in a 4d N=2{sup ∗} theory, mirroring the construction of Seifert manifold invariants via Dehn surgery. This is extended to include links in the Seifert manifold by the insertion of supersymmetric Wilson-’t Hooft loops in the 4d N=2{sup ∗} theory. In the presence of a mass parameter for the distinguished flavour symmetry, we recover aspects of refined Chern-Simons theory with complex gauge group, and in particular construct an analytic continuation of the S-matrix of refined Chern-Simons theory.
Multiple Membranes in M-theory
Bagger, Jonathan; Mukhi, Sunil; Papageorgakis, Constantinos
2013-01-01
We review developments in the theory of multiple, parallel membranes in M-theory. After discussing the inherent difficulties pertaining to a maximally supersymmetric lagrangian formulation with the appropriate field content and symmetries, we discuss how introducing the concept of 3-algebras allows for such a description. Different choices of 3-algebras lead to distinct classes of 2+1 dimensional theories with varying degrees of supersymmetry. We then describe how these are equivalent to a type of conventional superconformal Chern-Simons gauge theories at level k, coupled to bifundamental matter. Analysing the physical properties of these theories leads to the identification of a certain subclass of models with configurations of M2-branes in Z_k orbifolds of M-theory. In addition these models give rise to a whole new sector of the gauge/gravity duality in the form of an AdS_4/CFT_3 correspondence. We also discuss mass deformations, higher derivative corrections as well as the possibility of extracting informa...
Matrix effective theories of the fractional quantum Hall effect
International Nuclear Information System (INIS)
Cappelli, Andrea; Rodriguez, Ivan D
2009-01-01
The present understanding of nonperturbative ground states in the fractional quantum Hall effect is based on effective theories of the Jain 'composite fermion' excitations. We review the approach based on matrix variables, i.e. D0 branes, originally introduced by Susskind and Polychronakos. We show that the Maxwell-Chern-Simons matrix gauge theory provides a matrix generalization of the quantum Hall effect, where the composite-fermion construction naturally follows from gauge invariance. The matrix ground states obtained by suitable projections of higher Landau levels are found to be in one-to-one correspondence with the Laughlin and Jain hierarchical states. The matrix theory possesses a physical limit for commuting matrices that could be reachable while staying in the same phase.
Onset of dynamical chaos in topologically massive gauge theories
International Nuclear Information System (INIS)
Giansanti, A.; Simic, P.D.
1988-01-01
The onset of dynamical chaos is studied numerically in (2+1)-dimensional non-Abelian field theory with the Chern-Simons topological term. In the limit of strong fields, slowly varying in space (spatially homogeneous fields), this theory is an analog to a system of three charged particles moving in a plane in an orthogonal magnetic field and under the influence of a quartic potential. The ''phase transition'' (order chaos) is observed within a narrow energy range. The threshold of the transition depends on the sign of the angular momentum of the field reflecting parity violation in the underlying field theory. The transition region is investigated in some detail and the hyperfine structure of order-chaos-order-... transitions is observed suggesting the necessity of probabilistic description
(2 + 1)-dimensional interacting model of two massless spin-2 fields as a bi-gravity model
Hoseinzadeh, S.; Rezaei-Aghdam, A.
2018-06-01
We propose a new group-theoretical (Chern-Simons) formulation for the bi-metric theory of gravity in (2 + 1)-dimensional spacetime which describe two interacting massless spin-2 fields. Our model has been formulated in terms of two dreibeins rather than two metrics. We obtain our Chern-Simons gravity model by gauging mixed AdS-AdS Lie algebra and show that it has a two dimensional conformal field theory (CFT) at the boundary of the anti de Sitter (AdS) solution. We show that the central charge of the dual CFT is proportional to the mass of the AdS solution. We also study cosmological implications of our massless bi-gravity model.
Topologically massive gauge theories and their dual factorized gauge-invariant formulation
International Nuclear Information System (INIS)
Bertrand, Bruno; Govaerts, Jan
2007-01-01
There exists a well-known duality between the Maxwell-Chern-Simons theory and the 'self-dual' massive model in (2 + 1) dimensions. This dual description may be extended to topologically massive gauge theories (TMGT) for forms of arbitrary rank and in any dimension. This communication introduces the construction of this type of duality through a reparametrization of the 'master' theory action. The dual action thereby obtained preserves the full gauge symmetry structure of the original theory. Furthermore, the dual action is factorized into a propagating sector of massive gauge-invariant variables and a decoupled sector of gauge-variant variables defining a pure topological field theory. Combining the results obtained within the Lagrangian and Hamiltonian formulations, a completed structure for a gauge-invariant dual factorization of TMGT is thus achieved. (fast track communication)
Aspects Topologiques de la Theorie des Champs et leurs Applications
Caenepeel, Didier
This thesis is dedicated to the study of various topological aspects of field theory, and is divided in three parts. In two space dimensions the possibility of fractional statistics can be implemented by adding an appropriate "fictitious" electric charge and magnetic flux to each particle (after which they are known as anyons). Since the statistical interaction is rather difficult to handle, a mean-field approximation is used in order to describe a gas of anyons. We derive a criterion for the validity of this approximation using the inherent feature of parity violation in the scattering of anyons. We use this new method in various examples of anyons and show both analytically and numerically that the approximation is justified if the statistical interaction is weak, and that it must be more weak for boson-based than for fermion-based anyons. Chern-Simons theories give an elegant implementation of anyonic properties in field theories, which permits the emergence of new mechanisms for anyon superconductivity. Since it is reasonable to think that superconductivity is a low energy phenomenon, we have been interested in non-relativistic C-S systems. We present the scalar field effective potential for non-relativistic matter coupled to both Abelian and non-Abelian C-S gauge fields. We perform the calculations using functional methods in background fields. Finally, we compute the scalar effective potential in various gauges and treat divergences with various regularization schemes. In three space dimensions, a generalization of Chern-Simons theory may be achieved by introducing an antisymmetric tensor gauge field. We use these theories, called B wedge F theories, to present an alternative to the Higgs mechanism to generate masses for non-Abelian gauge fields. The initial Lagrangian is composed of a fermion with current-current and dipole-dipole type self -interactions minimally coupled to non-Abelian gauge fields. The mass generation occurs upon the fermionic functional
Sequences of extremal radially excited rotating black holes.
Blázquez-Salcedo, Jose Luis; Kunz, Jutta; Navarro-Lérida, Francisco; Radu, Eugen
2014-01-10
In the Einstein-Maxwell-Chern-Simons theory the extremal Reissner-Nordström solution is no longer the single extremal solution with vanishing angular momentum, when the Chern-Simons coupling constant reaches a critical value. Instead a whole sequence of rotating extremal J=0 solutions arises, labeled by the node number of the magnetic U(1) potential. Associated with the same near horizon solution, the mass of these radially excited extremal solutions converges to the mass of the extremal Reissner-Nordström solution. On the other hand, not all near horizon solutions are also realized as global solutions.
Mathematical aspects of quantum field theories
Strobl, Thomas
2015-01-01
Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homolo...
Noncompact symmetries in string theory
International Nuclear Information System (INIS)
Maharana, J.; Schwarz, J.H.
1993-01-01
Noncompact groups, similar to those that appeared in various supergravity theories in the 1970's have been turning up in recent studies of string theory. First it was discovered that moduli spaces of toroidal compactification are given by noncompact groups modded out by their maximal compact subgroups and discrete duality groups. Then it was found that many other moduli spaces have analogous descriptions. More recently, noncompact group symmetries have turned up in effective actions used to study string cosmology and other classical configurations. This paper explores these noncompact groups in the case of toroidal compactification both from the viewpoint of low-energy effective field theory, using the method of dimensional reduction, and from the viewpoint of the string theory world-sheet. The conclusion is that all these symmetries are intimately related. In particular, we find that Chern-Simons terms in the three-form field strength H μνρ play a crucial role. (orig.)
International Nuclear Information System (INIS)
Coman, Ioana; Teschner, Joerg
2015-05-01
Non-perturbative aspects of N=2 supersymmetric gauge theories of class S are deeply encoded in the algebra of functions on the moduli space M flat of at SL(N)-connections on Riemann surfaces. Expectation values of Wilson and 't Hooft line operators are related to holonomies of flat connections, and expectation values of line operators in the low-energy effective theory are related to Fock-Goncharov coordinates on M flat . Via the decomposition of UV line operators into IR line operators, we determine their noncommutative algebra from the quantization of Fock-Goncharov Laurent polynomials, and find that it coincides with the skein algebra studied in the context of Chern-Simons theory. Another realization of the skein algebra is generated by Verlinde network operators in Toda field theory. Comparing the spectra of these two realizations provides non-trivial support for their equivalence. Our results can be viewed as evidence for the generalization of the AGT correspondence to higher-rank class S theories.
On the Pulsating Strings in AdS4×ℂℙ3
Directory of Open Access Journals (Sweden)
H. Dimov
2009-01-01
we quasiclassically quantize the theory and obtain the first corrections to the energy. The latter, due to AdS/CFT correspondence, is supposed to give the anomalous dimensions of operators of the gauge theory dual 𝒩=6 Chern-Simons theory.
Gauge and integrable theories in loop spaces
International Nuclear Information System (INIS)
Ferreira, L.A.; Luchini, G.
2012-01-01
We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes theorems for p-form connections, and its appropriate mathematical language is that of loop spaces. The equations of motion are written as the equality of a hyper-volume ordered integral to a hyper-surface ordered integral on the border of that hyper-volume. The approach applies to integrable field theories in (1+1) dimensions, Chern-Simons theories in (2+1) dimensions, and non-abelian gauge theories in (2+1) and (3+1) dimensions. The results presented in this paper are relevant for the understanding of global properties of those theories. As a special byproduct we solve a long standing problem in (3+1)-dimensional Yang-Mills theory, namely the construction of conserved charges, valid for any solution, which are invariant under arbitrary gauge transformations.
International Nuclear Information System (INIS)
Mansouri, F.; Suranyi, P; Wijewardhana, L.C.R.
1991-10-01
In the test particle approximation, the scattering amplitude for two-particle scattering in (2+1)-dimensional Chern-Simons-Witten gravity and supergravity was computed and compared to the corresponding metric solutions. The formalism was then extended to the exact gauge theoretic treatment of the two-particle scattering problem and compared to 't Hooft's results from the metric approach. We have studied dynamical symmetry breaking in 2+1 dimensional field theories. We have analyzed strong Extended Technicolor (ETC) models where the ETC coupling is close to a critical value. There are effective scalar fields in each of the theories. We have worked our how such scalar particles can be produced and how they decay. The φ 4 field theory was investigated in the Schrodinger representation. The critical behavior was extracted in an arbitrary number of dimensions in second order of a systematic truncation approximation. The correlation exponent agrees with known values within a few percent
A general action for topological quantum field theories
International Nuclear Information System (INIS)
Dayi, O.F.
1989-03-01
Topological field theories can be formulated by beginning from a higher dimensional action. The additional dimension is an unphysical time parameter and the action is the derivative of a functional W with respect to this variable. In the d = 4 case, it produces actions which are shown to give topological quantum field theory after gauge fixing. In d = 3 this action leads to the Hamiltonian, which yields the Floer groups if the additional parameter is treated as physical when W is the pure Chern-Simons action. This W can be used to define a topological quantum field theory in d = 3 by treating the additional parameter as unphysical. The BFV-BRST operator quantization of this theory yields to an enlarged system which has only first class constraints. This is not identical to the previously introduced d = 3 topological quantum field theory, even if it is shown that the latter theory also gives the theory which we began with, after a partial gauge fixing. (author). 18 refs
Modifications of Einstein's theory of gravity at large distances
2015-01-01
In the last few years modified gravity theories have been proposed as extensions of Einstein's theory of gravity. Their main motivation is to explain the latest cosmological and astrophysical data on dark energy and dark matter. The study of general relativity at small scales has already produced important results (cf e.g. LNP 863 Quantum Gravity and Quantum Cosmology) while its study at large scales is challenging because recent and upcoming observational results will provide important information on the validity of these modified theories. In this volume, various aspects of modified gravity at large scales will be discussed: high-curvature gravity theories; general scalar-tensor theories; Galileon theories and their cosmological applications; F(R) gravity theories; massive, new massive and topologically massive gravity; Chern-Simons modifications of general relativity (including holographic variants) and higher-spin gravity theories, to name but a few of the most important recent developments. Edite...
Three-dimensional spin-3 theories based on general kinematical algebras
Energy Technology Data Exchange (ETDEWEB)
Bergshoeff, Eric [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Grumiller, Daniel; Prohazka, Stefan [Institute for Theoretical Physics, TU Wien,Wiedner Hauptstrasse 8-10/136, A-1040 Vienna (Austria); Rosseel, Jan [Albert Einstein Center for Fundamental Physics, University of Bern,Sidlerstrasse 5, 3012 Bern (Switzerland); Faculty of Physics, University of Vienna,Boltzmanngasse 5, A-1090 Vienna (Austria)
2017-01-25
We initiate the study of non- and ultra-relativistic higher spin theories. For sake of simplicity we focus on the spin-3 case in three dimensions. We classify all kinematical algebras that can be obtained by all possible Inönü-Wigner contraction procedures of the kinematical algebra of spin-3 theory in three dimensional (anti-) de Sitter space-time. We demonstrate how to construct associated actions of Chern-Simons type, directly in the ultra-relativistic case and by suitable algebraic extensions in the non-relativistic case. We show how to give these kinematical algebras an infinite-dimensional lift by imposing suitable boundary conditions in a theory we call “Carroll Gravity”, whose asymptotic symmetry algebra turns out to be an infinite-dimensional extension of the Carroll algebra.
Low dimensional field theories and condensed matter physics
International Nuclear Information System (INIS)
Nagaoka, Yosuke
1992-01-01
This issue is devoted to the Proceedings of the Fourth Yukawa International Seminar (YKIS '91) on Low Dimensional Field Theories and Condensed Matter Physics, which was held on July 28 to August 3 in Kyoto. In recent years there have been great experimental discoveries in the field of condensed matter physics: the quantum Hall effect and the high temperature superconductivity. Theoretical effort to clarify mechanisms of these phenomena revealed that they are deeply related to the basic problem of many-body systems with strong correlation. On the other hand, there have been important developments in field theory in low dimensions: the conformal field theory, the Chern-Simons gauge theory, etc. It was found that these theories work as a powerful method of approach to the problems in condensed matter physics. YKIS '91 was devoted to the study of common problems in low dimensional field theories and condensed matter physics. The 17 of the presented papers are collected in this issue. (J.P.N.)
The gravitational sector of 2d (0,2) F-theory vacua
International Nuclear Information System (INIS)
Lawrie, Craig; Schäfer-Nameki, Sakura; Weigand, Timo
2017-01-01
F-theory compactifications on Calabi-Yau fivefolds give rise to two-dimensional N=(0,2) supersymmetric field theories coupled to gravity. We explore the dilaton supergravity defined by the moduli sector of such compactifications. The massless moduli spectrum is found by uplifting Type IIB compactifications on Calabi-Yau fourfolds. This spectrum matches expectations from duality with M-theory on the same elliptic fibration. The latter defines an N=2 Supersymmetric Quantum Mechanics related to the 2d (0,2) F-theory supergravity via circle reduction. Using our recent results on the gravitational anomalies of duality twisted D3-branes wrapping curves in Calabi-Yau fivefolds we show that the F-theory spectrum is anomaly free. We match the classical Chern-Simons terms of the M-theory Super Quantum Mechanics to one-loop contributions to the effective action by S 1 reduction of the dual F-theory.
The gravitational sector of 2d (0,2) F-theory vacua
Energy Technology Data Exchange (ETDEWEB)
Lawrie, Craig [Institut für Theoretische Physik, Ruprecht-Karls-Universität,Philosophenweg 19, Heidelberg, 69120 (Germany); Schäfer-Nameki, Sakura [Mathematical Institute, University of Oxford,Woodstock Road, Oxford, OX2 6GG (United Kingdom); Weigand, Timo [Institut für Theoretische Physik, Ruprecht-Karls-Universität,Philosophenweg 19, Heidelberg, 69120 (Germany)
2017-05-19
F-theory compactifications on Calabi-Yau fivefolds give rise to two-dimensional N=(0,2) supersymmetric field theories coupled to gravity. We explore the dilaton supergravity defined by the moduli sector of such compactifications. The massless moduli spectrum is found by uplifting Type IIB compactifications on Calabi-Yau fourfolds. This spectrum matches expectations from duality with M-theory on the same elliptic fibration. The latter defines an N=2 Supersymmetric Quantum Mechanics related to the 2d (0,2) F-theory supergravity via circle reduction. Using our recent results on the gravitational anomalies of duality twisted D3-branes wrapping curves in Calabi-Yau fivefolds we show that the F-theory spectrum is anomaly free. We match the classical Chern-Simons terms of the M-theory Super Quantum Mechanics to one-loop contributions to the effective action by S{sup 1} reduction of the dual F-theory.
International Nuclear Information System (INIS)
Xiu-Ming, Zhang; Yi-Shi, Duan
2010-01-01
In the light of the decomposition of the SU(2) gauge potential for I = 1/2, we obtain the SU(2) Chern-Simons current over S 4 , i.e. the vortex current in the effective field for the four-dimensional quantum Hall effect. Similar to the vortex excitations in the two-dimensional quantum Hall effect (2D FQH) which are generated from the zero points of the complex scalar field, in the 4D FQH, we show that the SU(2) Chern–Simons vortices are generated from the zero points of the two-component wave functions Ψ, and their topological charges are quantized in terms of the Hopf indices and Brouwer degrees of φ-mapping under the condition that the zero points of field Ψ are regular points. (condensed matter: electronicstructure, electrical, magnetic, and opticalproperties)
On the conformal higher spin unfolded equation for a three-dimensional self-interacting scalar field
Energy Technology Data Exchange (ETDEWEB)
Nilsson, Bengt E.W. [Fundamental Physics, Chalmers University of Technology,SE-412 96 Göteborg (Sweden)
2016-08-24
We propose field equations for the conformal higher spin system in three dimensions coupled to a conformal scalar field with a sixth order potential. Both the higher spin equation and the unfolded equation for the scalar field have source terms and are based on a conformal higher spin algebra which we treat as an expansion in multi-commutators. Explicit expressions for the source terms are suggested and subjected to some simple tests. We also discuss a cascading relation between the Chern-Simons action for the higher spin gauge theory and an action containing a term for each spin that generalizes the spin 2 Chern-Simons action in terms of the spin connection expressed in terms of the frame field. This cascading property is demonstrated in the free theory for spin 3 but should work also in the complete higher spin theory.
Topological anomalies for Seifert 3-manifolds
Energy Technology Data Exchange (ETDEWEB)
Imbimbo, Camillo [Dipartimento di Fisica, Università di Genova,Via Dodecaneso 33, 16146 Genova (Italy); INFN - Sezione di Genova,Via Dodecaneso 33, 16146, Genova (Italy); Rosa, Dario [School of Physics and Astronomy andCenter for Theoretical Physics Seoul National University,Seoul 151-747 (Korea, Republic of); Dipartimento di Fisica, Università di Milano-Bicocca,I-20126 Milano (Italy); INFN - Sezione di Milano-Bicocca,I-20126 Milano (Italy)
2015-07-14
We study globally supersymmetric 3d gauge theories on curved manifolds by describing the coupling of 3d topological gauge theories, with both Yang-Mills and Chern-Simons terms in the action, to background topological gravity. In our approach, the Seifert condition for manifolds supporting global supersymmetry is elegantly deduced from the BRST transformations of topological gravity. A cohomological characterization of the geometrical moduli which affect the partition function is obtained. In the Seifert context the Chern-Simons topological (framing) anomaly is BRST trivial. We compute explicitly the corresponding local Wess-Zumino functional. As an application, we obtain the dependence on the Seifert moduli of the partition function of 3d supersymmetric gauge theory on the squashed sphere by solving the anomalous topological Ward identities, in a regularization independent way and without the need of evaluating any functional determinant.
The volume conjecture, perturbative knot invariants, and recursion relations for topological strings
Dijkgraaf, R.; Fuji, H.; Manabe, M.
2011-01-01
We study the relation between perturbative knot invariants and the free energies defined by topological string theory on the character variety of the knot. Such a correspondence between SL(2;C) Chern-Simons gauge theory and the topological open string theory was proposed earlier on the basis of the
Theoretical high energy physics
International Nuclear Information System (INIS)
Lee, T.D.
1992-01-01
This progress report discusses research by Columbia University staff in high energy physics. Some of the topics discussed are as follows: lattice gauge theory; quantum chromodynamics; parity doublets; solitons; baryon number violation; black holes; magnetic monopoles; gluon plasma; Chern-Simons theory; and the inflationary universe
Holographic entanglement entropy and gravitational anomalies
Castro, A.; Detournay, S.; Iqbal, N.; Perlmutter, E.
2014-01-01
We study entanglement entropy in two-dimensional conformal field theories with a gravitational anomaly. In theories with gravity duals, this anomaly is holographically represented by a gravitational Chern-Simons term in the bulk action. We show that the anomaly broadens the Ryu-Takayanagi minimal
Study of Yang–Mills–Chern–Simons theory in presence of the Gribov horizon
Energy Technology Data Exchange (ETDEWEB)
Canfora, Fabrizio, E-mail: canfora@cecs.cl [Centro de Estudios Cientificos (CECs), Valdivia (Chile); Universidad Andres Bello, Av. Republica 440, Santiago (Chile); Gomez, Arturo, E-mail: arturo.gomez@proyectos.uai.cl [Departamento de Ciencias, Facultad de Artes Liberales y Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Viña del Mar. (Chile); Sorella, Silvio Paolo, E-mail: sorella@uerj.br [UERJ, Universidade do Estado do Rio de Janeiro (UERJ), Instituto de Física Teórica, Rua São Francisco Xavier 524, 20550-013, Maracaná, Rio de Janeiro (Brazil); Vercauteren, David, E-mail: vercauteren.uerj@gmail.com [UERJ, Universidade do Estado do Rio de Janeiro (UERJ), Instituto de Física Teórica, Rua São Francisco Xavier 524, 20550-013, Maracaná, Rio de Janeiro (Brazil)
2014-06-15
The two-point gauge correlation function in Yang–Mills–Chern–Simons theory in three dimensional Euclidean space is analysed by taking into account the non-perturbative effects of the Gribov horizon. In this way, we are able to describe the confinement and de-confinement regimes, which naturally depend on the topological mass and on the gauge coupling constant of the theory. -- Highlights: •We implement the Gribov quantization to the Topologically massive Yang–Mills theory. •We find a modified propagator at strong coupling by the Gribov horizon. •The gauge propagator depends on the topological mass and the coupling constant. •By studying the gauge propagator we describe the confined–deconfined regimes.
Study of Yang–Mills–Chern–Simons theory in presence of the Gribov horizon
International Nuclear Information System (INIS)
Canfora, Fabrizio; Gomez, Arturo; Sorella, Silvio Paolo; Vercauteren, David
2014-01-01
The two-point gauge correlation function in Yang–Mills–Chern–Simons theory in three dimensional Euclidean space is analysed by taking into account the non-perturbative effects of the Gribov horizon. In this way, we are able to describe the confinement and de-confinement regimes, which naturally depend on the topological mass and on the gauge coupling constant of the theory. -- Highlights: •We implement the Gribov quantization to the Topologically massive Yang–Mills theory. •We find a modified propagator at strong coupling by the Gribov horizon. •The gauge propagator depends on the topological mass and the coupling constant. •By studying the gauge propagator we describe the confined–deconfined regimes
Gauge theories and integrable lattice models
International Nuclear Information System (INIS)
Witten, E.
1989-01-01
Investigations of new knot polynomials discovered in the last few years have shown them to be intimately connected with soluble models of two dimensional lattice statistical mechanics. In this paper, these results, which in time may illuminate the whole question of why integrable lattice models exist, are reconsidered from the point of view of three dimensional gauge theory. Expectation values of Wilson lines in three dimensional Chern-Simons gauge theories can be computed by evaluating the partition functions of certain lattice models on finite graphs obtained by projecting the Wilson lines to the plane. The models in question - previously considered in both the knot theory and statistical mechanics literature - are IRF models in which the local Boltzmann weights are the matrix elements of braiding matrices in rational conformal field theories. These matrix elements, in turn, can be represented in three dimensional gauge theory in terms of the expectation value of a certain tetrahedral configuration of Wilson lines. This representation makes manifest a surprising symmetry of the braiding matrix elements in conformal field theory. (orig.)
Field theory approach to quantum hall effect
International Nuclear Information System (INIS)
Cabo, A.; Chaichian, M.
1990-07-01
The Fradkin's formulation of statistical field theory is applied to the Coulomb interacting electron gas in a magnetic field. The electrons are confined to a plane in normal 3D-space and also interact with the physical 3D-electromagnetic field. The magnetic translation group (MTG) Ward identities are derived. Using them it is shown that the exact electron propagator is diagonalized in the basis of the wave functions of the free electron in a magnetic field whenever the MTG is unbroken. The general tensor structure of the polarization operator is obtained and used to show that the Chern-Simons action always describes the Hall effect properties of the system. A general proof of the Streda formula for the Hall conductivity is presented. It follows that the coefficient of the Chern-Simons terms in the long-wavelength approximation is exactly given by this relation. Such a formula, expressing the Hall conductivity as a simple derivative, in combination with diagonal form of the full propagator allows to obtain a simple expressions for the filling factor and the Hall conductivity. Indeed, these results, after assuming that the chemical potential lies in a gap of the density of states, lead to the conclusion that the Hall conductivity is given without corrections by σ xy = νe 2 /h where ν is the filling factor. In addition it follows that the filling factor is independent of the magnetic field if the chemical potential remains in the gap. (author). 21 ref, 1 fig
Complexity growth in massive gravity theories, the effects of chirality, and more
Ghodrati, Mahdis
2017-11-01
To study the effect of parity violation on the rate of complexity growth, by using "complexity=action " conjecture, we find the complexity growth rates in different solutions of the chiral theory of topologically massive gravity (TMG) and parity-preserving theory of new massive gravity (NMG). Using the results, one can see that decreasing the parameter μ , which increases the effect of the Chern-Simons term and increases chirality, would increase the rate of growth of complexity. Also one can observe a stronger correlation between complexity growth and temperature rather than complexity growth and entropy. At the end we comment on the possible meaning of the deforming term of chiral Liouville action for the rate of complexity growth of warped conformal field theories in the tensor network renormalization picture.
Herbert A. Simon: Nobel Prize in Economic Sciences, 1978.
Leahey, Thomas H
2003-09-01
In 1978, Herbert A. Simon won the Nobel Prize in Economic Sciences, the same Nobel won by Daniel Kahneman in 2002. Simon's work in fact paved the way for Kahneman's Nobel. Although trained in political science and economics rather than psychology, Simon applied psychological ideas to economic theorizing. Classical and neoclassical economic theories assume that people are perfectly rational and strive to optimize economic outcomes. Simon argued that human rationality is constrained, not perfect, and that people seek satisfactory rather than ideal outcomes. Despite his Nobel, Simon felt isolated in economics and ultimately moved into psychology. Nevertheless, his ideas percolated through the economic community, so that Kahneman, whose research advanced Simon's broad perspective, could be the psychologist who won the Nobel in economics.
A topologically twisted index for three-dimensional supersymmetric theories
International Nuclear Information System (INIS)
Benini, Francesco; Zaffaroni, Alberto
2015-01-01
We provide a general formula for the partition function of three-dimensional N=2 gauge theories placed on S 2 ×S 1 with a topological twist along S 2 , which can be interpreted as an index for chiral states of the theories immersed in background magnetic fields. The result is expressed as a sum over magnetic fluxes of the residues of a meromorphic form which is a function of the scalar zero-modes. The partition function depends on a collection of background magnetic fluxes and fugacities for the global symmetries. We illustrate our formula in many examples of 3d Yang-Mills-Chern-Simons theories with matter, including Aharony and Giveon-Kutasov dualities. Finally, our formula generalizes to Ω-backgrounds, as well as two-dimensional theories on S 2 and four-dimensional theories on S 2 ×T 2 . In particular this provides an alternative way to compute genus-zero A-model topological amplitudes and Gromov-Witten invariants.
Path-integral invariants in abelian Chern–Simons theory
International Nuclear Information System (INIS)
Guadagnini, E.; Thuillier, F.
2014-01-01
We consider the U(1) Chern–Simons gauge theory defined in a general closed oriented 3-manifold M; the functional integration is used to compute the normalized partition function and the expectation values of the link holonomies. The non-perturbative path-integral is defined in the space of the gauge orbits of the connections which belong to the various inequivalent U(1) principal bundles over M; the different sectors of configuration space are labelled by the elements of the first homology group of M and are characterized by appropriate background connections. The gauge orbits of flat connections, whose classification is also based on the homology group, control the non-perturbative contributions to the mean values. The functional integration is carried out in any 3-manifold M, and the corresponding path-integral invariants turn out to be strictly related with the abelian Reshetikhin–Turaev surgery invariants
Higher spin resolution of a toy big bang
Krishnan, Chethan; Roy, Shubho
2013-08-01
Diffeomorphisms preserve spacetime singularities, whereas higher spin symmetries need not. Since three-dimensional de Sitter space has quotients that have big-bang/big-crunch singularities and since dS3-gravity can be written as an SL(2,C) Chern-Simons theory, we investigate SL(3,C) Chern-Simons theory as a higher-spin context in which these singularities might get resolved. As in the case of higher spin black holes in AdS3, the solutions are invariantly characterized by their holonomies. We show that the dS3 quotient singularity can be desingularized by an SL(3,C) gauge transformation that preserves the holonomy: this is a higher spin resolution the cosmological singularity. Our work deals exclusively with the bulk theory, and is independent of the subtleties involved in defining a CFT2 dual to dS3 in the sense of dS/CFT.
F-theory and 2d (0,2) theories
Energy Technology Data Exchange (ETDEWEB)
Schäfer-Nameki, Sakura [Department of Mathematics, King’s College London, The Strand, London WC2R 2LS (United Kingdom); Weigand, Timo [Institut für Theoretische Physik, Ruprecht-Karls-Universität,Philosophenweg 19, 69120 Heidelberg (Germany)
2016-05-11
F-theory compactified on singular, elliptically fibered Calabi-Yau five-folds gives rise to two-dimensional gauge theories preserving N=(0,2) supersymmetry. In this paper we initiate the study of such compactifications and determine the dictionary between the geometric data of the elliptic fibration and the 2d gauge theory such as the matter content in terms of (0,2) superfields and their supersymmetric couplings. We study this setup both from a gauge-theoretic point of view, in terms of the partially twisted 7-brane theory, and provide a global geometric description based on the structure of the elliptic fibration and its singularities. Global consistency conditions are determined and checked against the dual M-theory compactification to one dimension. This includes a discussion of gauge anomalies, the structure of the Green-Schwarz terms and the Chern-Simons couplings in the dual M-theory supersymmetric quantum mechanics. Furthermore, by interpreting the resulting 2d (0,2) theories as heterotic worldsheet theories, we propose a correspondence between the geometric data of elliptically fibered Calabi-Yau five-folds and the target space of a heterotic gauged linear sigma-model (GLSM). In particular the correspondence between the Landau-Ginsburg and sigma-model phase of a 2d (0,2) GLSM is realized via different T-branes or gluing data in F-theory.
Thermodynamics of Higher Spin Black Holes in AdS3
de Boer, J.; Jottar, J.I.
2014-01-01
We discuss the thermodynamics of recently constructed three-dimensional higher spin black holes in SL(N, R) × SL(N, R) Chern-Simons theory with generalized asymptotically-anti-de Sitter boundary conditions. From a holographic perspective, these bulk theories are dual to two-dimensional CFTs with WN
Temperature dependent anomalous statistics
International Nuclear Information System (INIS)
Das, A.; Panda, S.
1991-07-01
We show that the anomalous statistics which arises in 2 + 1 dimensional Chern-Simons gauge theories can become temperature dependent in the most natural way. We analyze and show that a statistic's changing phase transition can happen in these theories only as T → ∞. (author). 14 refs
Bootstrapping non-commutative gauge theories from L∞ algebras
Blumenhagen, Ralph; Brunner, Ilka; Kupriyanov, Vladislav; Lüst, Dieter
2018-05-01
Non-commutative gauge theories with a non-constant NC-parameter are investigated. As a novel approach, we propose that such theories should admit an underlying L∞ algebra, that governs not only the action of the symmetries but also the dynamics of the theory. Our approach is well motivated from string theory. We recall that such field theories arise in the context of branes in WZW models and briefly comment on its appearance for integrable deformations of AdS5 sigma models. For the SU(2) WZW model, we show that the earlier proposed matrix valued gauge theory on the fuzzy 2-sphere can be bootstrapped via an L∞ algebra. We then apply this approach to the construction of non-commutative Chern-Simons and Yang-Mills theories on flat and curved backgrounds with non-constant NC-structure. More concretely, up to the second order, we demonstrate how derivative and curvature corrections to the equations of motion can be bootstrapped in an algebraic way from the L∞ algebra. The appearance of a non-trivial A∞ algebra is discussed, as well.
Low-dimensional gravities as gauge theories with non-compact groups
International Nuclear Information System (INIS)
Cangeni, D.
1993-01-01
In another note presented in these Proceedings it is shown that the two main lineal gravities can be given a gauge formulation. If it is already known that one of them the Sitter model - is a dimensional reduction of a Chern-Simons model in (2+1) dimensions, it was not clear whether the other one - the extended Poincare model follows from a similar reduction. The purpose of this note is to show that this is indeed the case provide we start in 2+1 dimensions with an extension ISO(2,1) of the Poincare groups as gauge group of a Chern-Simons model. We first show that this model gives a new proposal for gravity in 2*1 dimensions, since we get classically the Einstein's equations. Performing then a dimensional reduction, we recover not only the extended Poincare model but also the de Sitter one; hence, both lineal gravities get unified in the reduced model. (Author) 6 refs
Ghost free dual vector theories in 2+1 dimensions
International Nuclear Information System (INIS)
Dalmazi, Denis
2006-01-01
We explore here the issue of duality versus spectrum equivalence in dual theories generated through the master action approach. Specifically we examine a generalized self-dual (GSD) model where a Maxwell term is added to the self-dual model. A gauge embedding procedure applied to the GSD model leads to a Maxwell-Chern-Simons (MCS) theory with higher derivatives. We show here that the latter contains a ghost mode contrary to the original GSD model. By figuring out the origin of the ghost we are able to suggest a new master action which interpolates between the local GSD model and a nonlocal MCS model. Those models share the same spectrum and are ghost free. Furthermore, there is a dual map between both theories at classical level which survives quantum correlation functions up to contact terms. The remarks made here may be relevant for other applications of the master action approach
Toward a proof of Montonen-Olive duality via multiple M2-branes
International Nuclear Information System (INIS)
Hashimoto, Koji; Tai, Ta-Sheng; Terashima, Seiji
2009-01-01
We derive 4-dimensional N = 4 U(N) supersymmetric Yang-Mills theory from a 3-dimensional Chern-Simons-matter theory with product gauge group (U(N)) 2n . The latter describes M2-branes probing an orbifold where a torus emerges in a scaling limit. It is expected that the SL(2,Z) duality of the 4-dimensional Yang-Mills theory will be shown in M-theory point of view since it is trivially realized as modular transformations of the torus. Indeed, starting from one single Chern-Simons-matter theory, we find infinitely many equivalent 4-dimensional theories differing up to T-transformation of the SL(2,Z) redefinition of the gauge coupling τ = θ/2π + 4πi/g 2 and a parity transformation in 4 dimensions. Although S-transformation can not be shown in our work, it is important that a part of the SL(2,Z) transformation is realized via the M2-brane action. Thus we think our work can be a step toward a proof of Montonen-Olive duality via M2-branes.
Toward a proof of Montonen-Olive duality via multiple M2-branes
Hashimoto, Koji; Tai, Ta-Sheng; Terashima, Seiji
2009-04-01
We derive 4-dimensional Script N = 4 U(N) supersymmetric Yang-Mills theory from a 3-dimensional Chern-Simons-matter theory with product gauge group (U(N))2n. The latter describes M2-branes probing an orbifold where a torus emerges in a scaling limit. It is expected that the SL(2,Z) duality of the 4-dimensional Yang-Mills theory will be shown in M-theory point of view since it is trivially realized as modular transformations of the torus. Indeed, starting from one single Chern-Simons-matter theory, we find infinitely many equivalent 4-dimensional theories differing up to T-transformation of the SL(2,Z) redefinition of the gauge coupling τ = θ/2π + 4πi/g2 and a parity transformation in 4 dimensions. Although S-transformation can not be shown in our work, it is important that a part of the SL(2,Z) transformation is realized via the M2-brane action. Thus we think our work can be a step toward a proof of Montonen-Olive duality via M2-branes.
International Nuclear Information System (INIS)
Moore, G.; Seiberg, N.
1990-01-01
We review some recent results in two dimensional Rational Conformal Field Theory. We discuss these theories as generalization of group theory. The relation to a three dimensional topological theory is explained and the particular example of the Chern-Simons-Witten theory is analyzed in detail. This study leads to a natural conjecture regarding the classification of all RCFT's. (author). 64 refs, 4 figs
Theoretical high energy physics
International Nuclear Information System (INIS)
Lee, T.D.
1991-01-01
This report discusses theoretical research in high energy physics at Columbia University. Some of the research topics discussed are: quantum chromodynamics with dynamical fermions; lattice gauge theory; scattering of neutrinos by photons; atomic physics constraints on the properties of ultralight-ultraweak gauge bosons; black holes; Chern- Simons physics; S-channel theory of superconductivity; charged boson system; gluon-gluon interactions; high energy scattering in the presence of instantons; anyon physics; causality constraints on primordial magnetic manopoles; charged black holes with scalar hair; properties of Chern-Aimona-Higgs solitons; and extended inflationary universe
Refined large N duality for knots
DEFF Research Database (Denmark)
Kameyama, Masaya; Nawata, Satoshi
We formulate large N duality of U(N) refined Chern-Simons theory with a torus knot/link in S³. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string theory with D4-branes on the Ω-background. This form enables us to relate...
Descendants of the Chiral Anomaly
Jackiw, R.
2000-01-01
Chern-Simons terms are well-known descendants of chiral anomalies, when the latter are presented as total derivatives. Here I explain that also Chern-Simons terms, when defined on a 3-manifold, may be expressed as total derivatives.
The wave function behavior of the open topological string partition function on the conifold
International Nuclear Information System (INIS)
Kashani-Poor, Amir-Kian
2007-01-01
We calculate the topological string partition function to all genus on the conifold, in the presence of branes. We demonstrate that the partition functions for different brane backgrounds (smoothly connected along a quantum corrected moduli space) can be interpreted as the same wave function in different polarizations. This behavior has a natural interpretation in the Chern-Simons target space description of the topological theory. Our detailed analysis however indicates that non-perturbatively, a modification of real Chern-Simons theory is required to capture the correct target space theory of the topological string. We perform our calculations in the framework of a free fermion representation of the open topological string, demonstrating that this framework extends beyond the simple C 3 geometry. The notion of a fermionic brane creation operator arises in this setting, and we study to what extent the wave function properties of the partition function can be extended to this operator
Edge modes in the fractional quantum Hall effect without extra edge fermions
Lima, G. L. S.; Dias, S. A.
2011-05-01
We show that the Chern-Simons-Landau-Ginsburg theory that describes the quantum Hall effect on a bounded sample is anomaly free and thus does not require the addition of extra chiral fermions on the boundary to restore local gauge invariance.
Chiral topological excitons in a Chern band insulator
Chen, Ke; Shindou, Ryuichi
2017-10-01
A family of semiconductors called Chern band insulators are shown to host exciton bands with nonzero topological Chern integers and chiral exciton edge modes. Using a prototypical two-band Chern insulator model, we calculate a cross-correlation function to obtain the exciton bands and their Chern integers. The lowest exciton band acquires Chern integers such as ±1 and ±2 in the electronic Chern insulator phase. The nontrivial topology can be experimentally observed both by a nonlocal optoelectronic response of exciton edge modes and by a phase shift in the cross-correlation response due to the bulk mode. Our result suggests that magnetically doped HgTe, InAs/GaSb quantum wells, and (Bi,Sb)2Te3 thin films are promising candidates for a platform of topological excitonics.
The theory of anyonic superconductivity
International Nuclear Information System (INIS)
Lukken, J.D.; Sonnenschien, J.; Weiss, N.
1991-01-01
Particles in two spatial dimensions with fractional statistics known, generically, as anyons, have been of interest to particle physicists for nearly ten years. A major change in the direction of research occurred when it was discovered that anyons could play a role as quasiparticles in condensed-matter systems. This was originally discovered to be the case in systems exhibiting the Fractional Quantum Hall Effect. The application of anyons to condensed-matter systems received yet another boost when it was discovered by Laughlin that even an ideal gas of anyons was a superfluid and, as a result, a gas of charged anyons would be a superconductor. This led immediately to attempts to explain the superconductivity of high-T c materials which are layered ceramics in terms of anyons. The main challenge was to find a reasonable model for these materials which has quasiparticles obeying anyonic statistics. The goal of this article is to review the theory of anyonic superconductivity and its possible relation to high-T c materials. The emphasis in this review is on field-theoretical methods. In this paper the authors explain what an anyon is and how it can be modeled mathematically. The authors discuss the possible relationship between anyons and high-T c materials. The authors review several of the attempts to obtain anyonic quasiparticles from the Hubbard model which is commonly used to describe these materials. The authors describe the mathematical modeling of anyons in terms of their interaction with an Abelian gauge field with a Chern-Simons term. This description of anyons is used extensively in this article. The authors discuss the possible criteria for superconductivity in anyonic systems with particular emphasis on criteria which would be useful in the Chern-Simons description
Higher spins and matter interacting in dimension three
Czech Academy of Sciences Publication Activity Database
Kessel, P.; Lucena Gómez, Gustavo; Skvortsov, E.; Taronna, M.
2015-01-01
Roč. 2015, č. 11 (2015), s. 104 ISSN 1029-8479 R&D Projects: GA ČR(CZ) GA14-31689S Institutional support: RVO:68378271 Keywords : Higher Spin Gravity * Higher Spin Symmetry * AdS-CFT correspondence * Chern-Simons Theories Subject RIV: BD - Theory of Information Impact factor: 6.023, year: 2015
Remembering Roger I. Simon: A Pedagogy of Public Possibility
Farley, Lisa; Tarc, Aparna Mishra
2014-01-01
This special issue of "Canadian Social Studies" is dedicated to Roger I. Simon. Simon's scholarship bequeaths to theorists, teachers, and curators across Canada and beyond a theory of education that opens up responsibilities to past and present others. The papers gathered for this special issue address many of the difficulties that he…
International Nuclear Information System (INIS)
Aros, Rodrigo; Contreras, Mauricio
2006-01-01
In this work the Poincare-Chern-Simons and anti-de Sitter-Chern-Simons gravities are studied. For both, a solution that can be cast as a black hole with manifest torsion is found. Those solutions resemble Schwarzschild and Schwarzschild-AdS solutions, respectively
Political and Legal Doctrine of Simon Bolivar
Directory of Open Access Journals (Sweden)
Mixail V. Fedorov
2014-03-01
Full Text Available Present article is devoted to the legal, political and constitutional ideas of the outstanding leader of war of independence in Latin America Simon Bolivar that was called by his countrymen and contemporaries to be a LIBERATOR. In the present article author discusses complex genesis and evolution of the political and legal doctrine of Simon Bolivar. Review is conducted by author in the context of developing theory and practice of Latin American constitutionalism in the XIX century. Author conceptualized and revealed basic historical patterns of formation and development of Latin American countries during the War of Independence (1810-1826 period. Author conducted comprehensive analysis of the draft constitution which was developed by Simon Bolivar for the newly independent states of Latin America and reveals theoretical and practical problem of choosing Simon Bolivar republican form of government, such as a peculiar institution in the form of principle of the separation of powers, containing the fourth power. Author focuses on the questions of Simon Bolivar’s relationship to the constitutional institute of human rights, idea of relationship between state and church. Article also researches many other political, legal and constitutional ideas of Simon Bolivar, present views of historians, lawyers, political scientists, statesmen and public activists.
Topologically massive gravity and Ricci-Cotton flow
Energy Technology Data Exchange (ETDEWEB)
Lashkari, Nima; Maloney, Alexander, E-mail: lashkari@physics.mcgill.ca, E-mail: maloney@physics.mcgill.ca [McGill Physics Department, 3600 rue University, Montreal, QC H3A 2T8 (Canada)
2011-05-21
We consider topologically massive gravity (TMG), which is three-dimensional general relativity with a cosmological constant and a gravitational Chern-Simons term. When the cosmological constant is negative the theory has two potential vacuum solutions: anti-de Sitter space and warped anti-de Sitter space. The theory also contains a massive graviton state which renders these solutions unstable for certain values of the parameters and boundary conditions. We study the decay of these solutions due to the condensation of the massive graviton mode using Ricci-Cotton flow, which is the appropriate generalization of Ricci flow to TMG. When the Chern-Simons coupling is small the AdS solution flows to warped AdS by the condensation of the massive graviton mode. When the coupling is large the situation is reversed, and warped AdS flows to AdS. Minisuperspace models are constructed where these flows are studied explicitly.
Topologically massive gravity and Ricci-Cotton flow
International Nuclear Information System (INIS)
Lashkari, Nima; Maloney, Alexander
2011-01-01
We consider topologically massive gravity (TMG), which is three-dimensional general relativity with a cosmological constant and a gravitational Chern-Simons term. When the cosmological constant is negative the theory has two potential vacuum solutions: anti-de Sitter space and warped anti-de Sitter space. The theory also contains a massive graviton state which renders these solutions unstable for certain values of the parameters and boundary conditions. We study the decay of these solutions due to the condensation of the massive graviton mode using Ricci-Cotton flow, which is the appropriate generalization of Ricci flow to TMG. When the Chern-Simons coupling is small the AdS solution flows to warped AdS by the condensation of the massive graviton mode. When the coupling is large the situation is reversed, and warped AdS flows to AdS. Minisuperspace models are constructed where these flows are studied explicitly.
Anomalous transport and holographic momentum relaxation
Copetti, Christian; Fernández-Pendás, Jorge; Landsteiner, Karl; Megías, Eugenio
2017-09-01
The chiral magnetic and vortical effects denote the generation of dissipationless currents due to magnetic fields or rotation. They can be studied in holographic models with Chern-Simons couplings dual to anomalies in field theory. We study a holographic model with translation symmetry breaking based on linear massless scalar field backgrounds. We compute the electric DC conductivity and find that it can vanish for certain values of the translation symmetry breaking couplings. Then we compute the chiral magnetic and chiral vortical conductivities. They are completely independent of the holographic disorder couplings and take the usual values in terms of chemical potential and temperature. To arrive at this result we suggest a new definition of energy-momentum tensor in presence of the gravitational Chern-Simons coupling.
Design of Chern insulating phases in honeycomb lattices
Pickett, Warren E.; Lee, Kwan-Woo; Pentcheva, Rossitza
2018-06-01
The search for robust examples of the magnetic version of topological insulators, referred to as quantum anomalous Hall insulators or simply Chern insulators, so far lacks success. Our groups have explored two distinct possibilities based on multiorbital 3d oxide honeycomb lattices. Each has a Chern insulating phase near the ground state, but materials parameters were not appropriate to produce a viable Chern insulator. Further exploration of one of these classes, by substituting open shell 3d with 4d and 5d counterparts, has led to realistic prediction of Chern insulating ground states. Here we recount the design process, discussing the many energy scales that are active in participating (or resisting) the desired Chern insulator phase.
On a Canonical Quantization of 3D Anti de Sitter Pure Gravity
Kim, Jihun
2015-10-14
We perform a canonical quantization of pure gravity on AdS3 using as a technical tool its equivalence at the classical level with a Chern-Simons theory with gauge group SL(2,R)xSL(2,R). We first quantize the theory canonically on an asymptotically AdS space --which is topologically the real line times a Riemann surface with one connected boundary. Using the "constrain first" approach we reduce canonical quantization to quantization of orbits of the Virasoro group and Kaehler quantization of Teichmuller space. After explicitly computing the Kaehler form for the torus with one boundary component and after extending that result to higher genus, we recover known results, such as that wave functions of SL(2,R) Chern-Simons theory are conformal blocks. We find new restrictions on the Hilbert space of pure gravity by imposing invariance under large diffeomorphisms and normalizability of the wave function. The Hilbert space of pure gravity is shown to be the target space of Conformal Field Theories with continuous sp...
Duality and modular invariance in rational conformal field theories
International Nuclear Information System (INIS)
Li Miao.
1990-03-01
We investigate the polynomial equations which should be satisfied by the duality data for a rational conformal field theory. We show that by these duality data we can construct some vector spaces which are isomorphic to the spaces of conformal blocks. One can construct explicitly the inner product for the former if one deals with a unitary theory. These vector spaces endowed with an inner product are the algebraic reminiscences of the Hilbert spaces in a Chern-Simons theory. As by-products, we show that the polynomial equations involving the modular transformations for the one-point blocks on the torus are not independent. And along the way, we discuss the reconstruction of the quantum group in a rational conformal theory. Finally, we discuss the solution of structure constants for a physical theory. Making some assumption, we obtain a neat solution. And this solution in turn implies that the quantum groups of the left sector and of the right sector must be the same, although the chiral algebras need not to be the same. Some examples are given. (orig.)
Instantons in Lifshitz field theories
Energy Technology Data Exchange (ETDEWEB)
Fujimori, Toshiaki; Nitta, Muneto [Department of Physics, and Research and Education Center for Natural Sciences, Keio University, Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521 (Japan)
2015-10-05
BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for “the superpotential” defining “the detailed balance condition”. The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kähler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4+1 dimensions, for which we take the Chern-Simons term as the superpotential.
Gravitational catalysis of merons in Einstein-Yang-Mills theory
Canfora, Fabrizio; Oh, Seung Hun; Salgado-Rebolledo, Patricio
2017-10-01
We construct regular configurations of the Einstein-Yang-Mills theory in various dimensions. The gauge field is of meron-type: it is proportional to a pure gauge (with a suitable parameter λ determined by the field equations). The corresponding smooth gauge transformation cannot be deformed continuously to the identity. In the three-dimensional case we consider the inclusion of a Chern-Simons term into the analysis, allowing λ to be different from its usual value of 1 /2 . In four dimensions, the gravitating meron is a smooth Euclidean wormhole interpolating between different vacua of the theory. In five and higher dimensions smooth meron-like configurations can also be constructed by considering warped products of the three-sphere and lower-dimensional Einstein manifolds. In all cases merons (which on flat spaces would be singular) become regular due to the coupling with general relativity. This effect is named "gravitational catalysis of merons".
Symmetries and gravitational Chern–Simons Lagrangian terms
International Nuclear Information System (INIS)
Bonora, L.; Cvitan, M.; Dominis Prester, P.; Pallua, S.; Smolić, I.
2013-01-01
We consider some general consequences of adding pure gravitational Chern–Simons term to manifestly diff-covariant theories of gravity, focusing essentially on spacetimes with D>3. Extending the result of a previous paper we enlarge the class of metrics for which the inclusion of a gravitational Chern–Simons term in the action does not affect solutions and corresponding physical quantities. In the case in which such solutions describe black holes (of general horizon topology) we show that the black hole entropy is also unchanged. We arrive at these conclusions by proving three general theorems and studying their consequences. One of the theorems states that the contribution of the gravitational Chern–Simons to the black hole entropy is invariant under local rescaling of the metric
Non-Abelian Kubo formula and the multiple time-scale method
International Nuclear Information System (INIS)
Zhang, X.; Li, J.
1996-01-01
The non-Abelian Kubo formula is derived from the kinetic theory. That expression is compared with the one obtained using the eikonal for a Chern endash Simons theory. The multiple time-scale method is used to study the non-Abelian Kubo formula, and the damping rate for longitudinal color waves is computed. copyright 1996 Academic Press, Inc
Discretization of 3d gravity in different polarizations
Dupuis, Maïté; Freidel, Laurent; Girelli, Florian
2017-10-01
We study the discretization of three-dimensional gravity with Λ =0 following the loop quantum gravity framework. In the process, we realize that different choices of polarization are possible. This allows us to introduce a new discretization based on the triad as opposed to the connection as in the standard loop quantum gravity framework. We also identify the classical nontrivial symmetries of discrete gravity, namely the Drinfeld double, given in terms of momentum maps. Another choice of polarization is given by the Chern-Simons formulation of gravity. Our framework also provides a new discretization scheme of Chern-Simons, which keeps track of the link between the continuum variables and the discrete ones. We show how the Poisson bracket we recover between the Chern-Simons holonomies allows us to recover the Goldman bracket. There is also a transparent link between the discrete Chern-Simons formulation and the discretization of gravity based on the connection (loop gravity) or triad variables (dual loop gravity).
Phase transitions in a gas of anyons
International Nuclear Information System (INIS)
MacKenzie, R.; Nebia-Rahal, F.; Paranjape, M. B.; Richer, J.
2010-01-01
We continue our numerical Monte Carlo simulation of a gas of closed loops on a 3 dimensional lattice, however, now in the presence of a topological term added to the action which corresponds to the total linking number between the loops. We compute the linking number using a novel approach employing certain notions from knot theory. Adding the topological term converts the particles into anyons. Interpreting the model as an effective theory that describes the 2+1-dimensional Abelian Higgs model in the asymptotic strong-coupling regime, the topological linking number simply corresponds to the addition to the action of the Chern-Simons term. The system continues to exhibit a phase transition as a function of the vortex mass as it becomes small. We find the following new results. The Chern-Simons term has no effect on the Wilson loop. On the other hand, it does effect the 't Hooft loop of a given configuration, adding the linking number of the 't Hooft loop with all of the dynamical vortex loops. We find the unexpected result that both the Wilson loop and the 't Hooft loop exhibit a perimeter law even though there are no massless particles in the theory, in both phases of the theory. It should be noted that our method suffers from numerical instabilities if the coefficient of the Chern-Simons term is too large; thus, we have restricted our results to small values of this parameter. Furthermore, interpreting the lattice loop gas as an effective theory describing the Abelian Higgs model is only known to be true in the infinite coupling limit; for strong but finite coupling this correspondence is only a conjecture, the validity of which is beyond the scope of this article.
Zero-modes of non-Abelian solitons in three-dimensional gauge theories
International Nuclear Information System (INIS)
Eto, Minoru; Gudnason, Sven Bjarke
2011-01-01
We study non-Abelian solitons of the Bogomol'nyi type in N=2 (d = 2 + 1) supersymmetric Chern-Simons (CS) and Yang-Mills (YM) theory with a generic gauge group. In CS theory, we find topological, non-topological and semi-local (non-)topological vortices of non-Abelian kinds in unbroken, broken and partially broken vacua. We calculate the number of zero-modes using an index theorem and then we apply the moduli matrix formalism to realize the moduli parameters. For the topological solitons we exhaust all the moduli while we study several examples of the non-topological and semi-local solitons. We find that the zero-modes of the topological solitons are governed by the moduli matrix H 0 only and those of the non-topological solitons are governed by both H 0 and the gauge invariant field Ω. We prove local uniqueness of the master equation in the YM case and finally compare all results between the CS and YM theories.
Workshop on quantum stochastic differential equations for the quantum simulation of physical systems
2016-09-22
that would be complimentary to the efforts at ARL. One the other hand, topological quantum field theories have a dual application to topological...Witten provided a path-integral definition of the Jones polynomial using a three-dimensional Chern-Simons quantum field theory (QFT) based on a non...topology, quantum field theory , quantum stochastic differential equations, quantum computing REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S REPORT
Theoretical high energy physics
International Nuclear Information System (INIS)
Lee, T.D.
1990-05-01
This report discusses progress on theoretical high energy physics at Columbia University in New York City. Some of the topics covered are: Chern-Simons gauge field theories; dynamical fermion QCD calculations; lattice gauge theory; the standard model of weak and electromagnetic interactions; Boson-fermion model of cuprate superconductors; S-channel theory of superconductivity and axial anomaly and its relation to spin in the parton model
SU(5)-invariant decomposition of ten-dimensional Yang-Mills supersymmetry
Baulieu, Laurent
2011-01-01
The N=1,d=10 superYang-Mills action is constructed in a twisted form, using SU(5)-invariant decomposition of spinors in 10 dimensions. The action and its off-shell closed twisted scalar supersymmetry operator Q derive from a Chern-Simons term. The action can be decomposed as the sum of a term in the cohomology of Q and of a term that is Q-exact. The first term is a fermionic Chern-Simons term for a twisted component of the Majorana-Weyl gluino and it is related to the second one by a twisted vector supersymmetry with 5 parameters. The cohomology of Q and some topological observables are defined from descent equations. In this SU(5)
Canonical formulations of full nonlinear topologically massive gravity
International Nuclear Information System (INIS)
Deser, S.; Xiang, X.
1991-01-01
First-order forms of the complete nonlinear Einstein plus Chern-Simons third-derivative-order action are exhibited in both metric and dreibein forms. The 'hamiltonians' are combinations of diffeomorphism and tangent space rotation generators as expected of generally covariant systems; the pure Chern-Simons hamiltonian has an additional, conformal transformation, term. These constraints reduce the apparent number of degrees of freedom to 1 and 0 respectively. The constraint algebras close, as required by this counting, without second-class constraints. The nature of the noninvariant terms in the Chern-Simons lagrangian density is discussed. For comparison, the linearized limit and the corresponding nonabelian vector action's canonical form are also given. (orig.)
Asymptotic symmetries, holography and topological hair
Mishra, Rashmish K.; Sundrum, Raman
2018-01-01
Asymptotic symmetries of AdS4 quantum gravity and gauge theory are derived by coupling the holographically dual CFT3 to Chern-Simons gauge theory and 3D gravity in a "probe" (large-level) limit. Despite the fact that the three-dimensional AdS4 boundary as a whole is consistent with only finite-dimensional asymptotic symmetries, given by AdS isometries, infinite-dimensional symmetries are shown to arise in circumstances where one is restricted to boundary subspaces with effectively two-dimensional geometry. A canonical example of such a restriction occurs within the 4D subregion described by a Wheeler-DeWitt wavefunctional of AdS4 quantum gravity. An AdS4 analog of Minkowski "super-rotation" asymptotic symmetry is probed by 3D Einstein gravity, yielding CFT2 structure (in a large central charge limit), via AdS3 foliation of AdS4 and the AdS3/CFT2 correspondence. The maximal asymptotic symmetry is however probed by 3D conformal gravity. Both 3D gravities have Chern-Simons formulation, manifesting their topological character. Chern-Simons structure is also shown to be emergent in the Poincare patch of AdS4, as soft/boundary limits of 4D gauge theory, rather than "put in by hand" as an external probe. This results in a finite effective Chern-Simons level. Several of the considerations of asymptotic symmetry structure are found to be simpler for AdS4 than for Mink4, such as non-zero 4D particle masses, 4D non-perturbative "hard" effects, and consistency with unitarity. The last of these in particular is greatly simplified because in some set-ups the time dimension is explicitly shared by each level of description: Lorentzian AdS4, CFT3 and CFT2. Relatedly, the CFT2 structure clarifies the sense in which the infinite asymptotic charges constitute a useful form of "hair" for black holes and other complex 4D states. An AdS4 analog of Minkowski "memory" effects is derived, but with late-time memory of earlier events being replaced by (holographic) "shadow" effects. Lessons
ADHM and the 4d quantum Hall effect
Barns-Graham, Alec; Dorey, Nick; Lohitsiri, Nakarin; Tong, David; Turner, Carl
2018-04-01
Yang-Mills instantons are solitonic particles in d = 4 + 1 dimensional gauge theories. We construct and analyse the quantum Hall states that arise when these particles are restricted to the lowest Landau level. We describe the ground state wavefunctions for both Abelian and non-Abelian quantum Hall states. Although our model is purely bosonic, we show that the excitations of this 4d quantum Hall state are governed by the Nekrasov partition function of a certain five dimensional supersymmetric gauge theory with Chern-Simons term. The partition function can also be interpreted as a variant of the Hilbert series of the instanton moduli space, counting holomorphic sections rather than holomorphic functions. It is known that the Hilbert series of the instanton moduli space can be rewritten using mirror symmetry of 3d gauge theories in terms of Coulomb branch variables. We generalise this approach to include the effect of a five dimensional Chern-Simons term. We demonstrate that the resulting Coulomb branch formula coincides with the corresponding Higgs branch Molien integral which, in turn, reproduces the standard formula for the Nekrasov partition function.
Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions
Directory of Open Access Journals (Sweden)
Derek K. Wise
2009-08-01
Full Text Available Einstein gravity in both 3 and 4 dimensions, as well as some interesting generalizations, can be written as gauge theories in which the connection is a Cartan connection for geometry modeled on a symmetric space. The relevant models in 3 dimensions include Einstein gravity in Chern-Simons form, as well as a new formulation of topologically massive gravity, with arbitrary cosmological constant, as a single constrained Chern-Simons action. In 4 dimensions the main model of interest is MacDowell-Mansouri gravity, generalized to include the Immirzi parameter in a natural way. I formulate these theories in Cartan geometric language, emphasizing also the role played by the symmetric space structure of the model. I also explain how, from the perspective of these Cartan-geometric formulations, both the topological mass in 3d and the Immirzi parameter in 4d are the result of non-simplicity of the Lorentz Lie algebra so(3,1 and its relatives. Finally, I suggest how the language of Cartan geometry provides a guiding principle for elegantly reformulating any 'gauge theory of geometry'.
M-theory potential from the G{sub 2} Hitchin functional in superspace
Energy Technology Data Exchange (ETDEWEB)
Becker, Katrin; Becker, Melanie; Guha, Sunny; III, William D. Linch [George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University,College Station, TX 77843 (United States); Robbins, Daniel [Department of Physics, University at Albany.1400 Washington Ave., Albany, NY 12222 (United States)
2016-12-16
We embed the component fields of eleven-dimensional supergravity into a superspace of the form X×Y where X is the standard 4D, N=1 superspace and Y is a smooth 7-manifold. The eleven-dimensional 3-form gives rise to a tensor hierarchy of superfields gauged by the diffeomorphisms of Y. It contains a natural candidate for a G{sub 2} structure on Y, and being a complex of superforms, defines a superspace Chern-Simons invariant. Adding to this a natural generalization of the Riemannian volume on X×Y and freezing the (superspin-(3/2) and 1) supergravity fields on X, we obtain an approximation to the eleven-dimensional supergravity action that suffices to compute the scalar potential. In this approximation the action is the sum of the superspace Chern-Simons term and a superspace generalization of the Hitchin functional for Y as a G{sub 2}-structure manifold. Integrating out auxiliary fields, we obtain the conditions for unbroken supersymmetry and the scalar potential. The latter reproduces the Einstein-Hilbert term on Y in a form due to Bryant.
International Nuclear Information System (INIS)
Ma Zhongshui; Su Zhaobin.
1992-09-01
By applying the Dirac quantization method, we build the constraint that all electrons are in the lowest Landau level into the Chern-Simons field theory approach for the fractional quantum Hall system and show that the constraint can be transmuted from hierarchy to hierarchy. For a finite system, we derive that the action for each hierarchy can be split into two parts: a surface part provides the action for the edge excitations while the remaining part is precisely the bulk action for the next hierarchy. An the action for the edge could be decoupled from the bulk only at the hierarchy filling. (author). 16 refs
Proceedings of the 14. Claude Itzykson Meeting-2009 recent advances in string theory
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Aharoni, O.; Arkani-Hamed, N.; Becker, K.; Berkovits, N.; Bern, Z.; De Boer, J.; Emparan, R.; Green, M.; Hartnoll, S.; Heckman, J.; Kachru, S.; Lambert, N.; Louis, J.; Marino, M.; Mathur, S.; McAllister, L.; McGreevy, J.; Polchinski, J.; Sen, A.; Weigand, T.
2009-01-01
This document is made up of the slides of the presentations. The titles of the 20 presentations are the following: 1) On d=3 Yang-Mills Chern-Simons theories with 'fractional branes' and their gravity duals; 2) Holography and the S-Matrix; 3) Torsional heterotic geometries; 4) Spin chains from the topological AdS 5 xS 5 string; 5) Harmony of Scattering Amplitudes: from N=4 Super-Yang-Mills Theory to N=8 Supergravity; 6) Quantum aspects of black holes; 7) Black-folds; 8) Supersymmetric String and Field Theory Scattering Amplitudes; 9) Quantum bosons for holographic superconductors; 10) The Point of E8 in F-theory GUTs; 11) Gauge/gravity duality and particle physics; 12) Coupling M2-branes to Background Fields; 13) Compactifications and Generalized Geometries; 14) Nonperturbative aspects of the topological string; 15) Lessons from the information paradox: 16) Inflation in String Theory; 17) Holographic descriptions of quantum liquids; 18) Holography from CFT; 19) Black hole hair removal; and 20) Type IIB GUT vacua and their F-theory uplift
(Non-)Abelian Kramers-Wannier duality and topological field theory
Severa, Pavol
2002-01-01
We study a connection between duality and topological field theories. First, 2d Kramers-Wannier duality is formulated as a simple 3d topological claim (more or less Poincare duality), and a similar formulation is given for higher-dimensional cases. In this form they lead to simple TFTs with boundary coloured in two colours. The statistical models live on the boundary of these TFTs, as in the CS/WZW or AdS/CFT correspondence. Classical models (Poisson-Lie T-duality) suggest a non-abelian generalization in the 2dcase, with abelian groups replaced by quantum groups. Amazingly, the TFT formulation solves the problem without computation: quantum groups appear in pictures, independently of the classical motivation. Connection with Chern-Simons theory appears at the symplectic level, and also in the pictures of the Drinfeld double: Reshetikhin-Turaev invariants of links in 3-manifolds, computed from the double, are included in these TFTs. All this suggests nice phenomena in higher dimensions.
Physics of F-theory compactifications without section
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Anderson, Lara B.; García-Etxebarria, Iñaki; Grimm, Thomas W.; Keitel, Jan
2014-01-01
We study the physics of F-theory compactifications on genus-one fibrations without section by using an M-theory dual description. The five-dimensional action obtained by considering M-theory on a Calabi-Yau threefold is compared with a six-dimensional F-theory effective action reduced on an additional circle. We propose that the six-dimensional effective action of these setups admits geometrically massive U(1) vectors with a charged hypermultiplet spectrum. The absence of a section induces NS-NS and R-R three-form fluxes in F-theory that are non-trivially supported along the circle and induce a shift-gauging of certain axions with respect to the Kaluza-Klein vector. In the five-dimensional effective theory the Kaluza-Klein vector and the massive U(1)s combine into a linear combination that is massless. This U(1) is identified with the massless U(1) corresponding to the multi-section of the Calabi-Yau threefold in M-theory. We confirm this interpretation by computing the one-loop Chern-Simons terms for the massless vectors of the five-dimensional setup by integrating out all massive states. A closed formula is found that accounts for the hypermultiplets charged under the massive U(1)s.
Computer calculation of Witten's 3-manifold invariant
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Freed, D.S.; Gompf, R.E.
1991-01-01
Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant. (orig.)
International Nuclear Information System (INIS)
Marmo, G.; Morandi, G.
1995-01-01
In this lecture some mathematical problems that arise when one deals with low-dimensional field theories, such as homotopy and topological invariants, differential calculus on Lie groups and coset spaces, fiber spaces and parallel transport, differential calculus on fiber bundles, sequences on principal bundles and Chern-Simons terms are discussed
Exploring Lovelock theory moduli space for Schrödinger solutions
Jatkar, Dileep P.; Kundu, Nilay
2016-09-01
We look for Schrödinger solutions in Lovelock gravity in D > 4. We span the entire parameter space and determine parametric relations under which the Schrödinger solution exists. We find that in arbitrary dimensions pure Lovelock theories have Schrödinger solutions of arbitrary radius, on a co-dimension one locus in the Lovelock parameter space. This co-dimension one locus contains the subspace over which the Lovelock gravity can be written in the Chern-Simons form. Schrödinger solutions do not exist outside this locus and on this locus they exist for arbitrary dynamical exponent z. This freedom in z is due to the degeneracy in the configuration space. We show that this degeneracy survives certain deformation away from the Lovelock moduli space.
Matrix models and stochastic growth in Donaldson-Thomas theory
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Szabo, Richard J. [Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS, United Kingdom and Maxwell Institute for Mathematical Sciences, Edinburgh (United Kingdom); Tierz, Miguel [Grupo de Fisica Matematica, Complexo Interdisciplinar da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, PT-1649-003 Lisboa (Portugal); Departamento de Analisis Matematico, Facultad de Ciencias Matematicas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid (Spain)
2012-10-15
We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kaehler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.
Matrix models and stochastic growth in Donaldson-Thomas theory
International Nuclear Information System (INIS)
Szabo, Richard J.; Tierz, Miguel
2012-01-01
We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kähler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.
Warped conformal field theory as lower spin gravity
Hofman, Diego M.; Rollier, Blaise
2015-08-01
Two dimensional Warped Conformal Field Theories (WCFTs) may represent the simplest examples of field theories without Lorentz invariance that can be described holographically. As such they constitute a natural window into holography in non-AdS space-times, including the near horizon geometry of generic extremal black holes. It is shown in this paper that WCFTs posses a type of boost symmetry. Using this insight, we discuss how to couple these theories to background geometry. This geometry is not Riemannian. We call it Warped Geometry and it turns out to be a variant of a Newton-Cartan structure with additional scaling symmetries. With this formalism the equivalent of Weyl invariance in these theories is presented and we write two explicit examples of WCFTs. These are free fermionic theories. Lastly we present a systematic description of the holographic duals of WCFTs. It is argued that the minimal setup is not Einstein gravity but an SL (2, R) × U (1) Chern-Simons Theory, which we call Lower Spin Gravity. This point of view makes manifest the definition of boundary for these non-AdS geometries. This case represents the first step towards understanding a fully invariant formalism for WN field theories and their holographic duals.
The topological B model as a twisted spinning particle
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Marcus, Neil; Yankielowicz, Shimon
1994-01-01
The B-twisted topological sigma model coupled to topological gravity is supposed to be described by an ordinary field theory: a type of holomorphic Chern-Simons theory for the open string, and the Kodaira-Spencer theory for the closed string. We show that the B model can be represented as a particle theory, obtained by reducing the sigma model to one dimension, and replacing the coupling to topological gravity by a coupling to a twisted one-dimensional supergravity. The particle can be defined on any Kaehler manifold - it does not require the Calabi-Yau condition - so it may provide a more generalized setting for the B model than the topological sigma model.The one-loop partition function of the particle can be written in terms of the Ray-Singer torsion of the manifold, and agrees with that of the original B model. After showing how to deform the Kaehler and complex structures in the particle, we prove the independence of this partition function on the Kaehler structure, and investigate the origin of the holomorphic anomaly. To define other amplitudes, one needs to introduce interactions into the particle. The particle will then define a field theory, which may or may not be the Chern-Simons or Kodaira-Spencer theories. ((orig.))
Soldering formalism in noncommutative field theory: a brief note
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Ghosh, Subir
2004-01-01
In this Letter, I develop the soldering formalism in a new domain--the noncommutative planar field theories. The soldering mechanism fuses two distinct theories showing opposite or complimentary properties of some symmetry, taking into account the interference effects. The above mentioned symmetry is hidden in the composite (or soldered) theory. In the present work it is shown that a pair of noncommutative Maxwell-Chern-Simons theories, having opposite signs in their respective topological terms, can be consistently soldered to yield the Proca model (Maxwell theory with a mass term) with corrections that are at least quadratic in the noncommutativity parameter. We further argue that this model can be thought of as the noncommutative generalization of the Proca theory of ordinary spacetime. It is well known that abelian noncommutative gauge theory bears a close structural similarity with non-abelian gauge theory. This fact is manifested in a non-trivial way if the present Letter is compared with existing literature, where soldering of non-abelian models are discussed. Thus the present work further establishes the robustness of the soldering programme. The subtle role played by gauge invariance (or the lack of it), in the above soldering process, is revealed in an interesting way
Topological insulators and superconductors from string theory
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Ryu, Shinsei; Takayanagi, Tadashi
2010-01-01
Topological insulators and superconductors in different spatial dimensions and with different discrete symmetries have been fully classified recently, revealing a periodic structure for the pattern of possible types of topological insulators and superconductors, both in terms of spatial dimensions and in terms of symmetry classes. It was proposed that K theory is behind the periodicity. On the other hand, D-branes, a solitonic object in string theory, are also known to be classified by K theory. In this paper, by inspecting low-energy effective field theories realized by two parallel D-branes, we establish a one-to-one correspondence between the K-theory classification of topological insulators/superconductors and D-brane charges. In addition, the string theory realization of topological insulators and superconductors comes naturally with gauge interactions, and the Wess-Zumino term of the D-branes gives rise to a gauge field theory of topological nature, such as ones with the Chern-Simons term or the θ term in various dimensions. This sheds light on topological insulators and superconductors beyond noninteracting systems, and the underlying topological field theory description thereof. In particular, our string theory realization includes the honeycomb lattice Kitaev model in two spatial dimensions, and its higher-dimensional extensions. Increasing the number of D-branes naturally leads to a realization of topological insulators and superconductors in terms of holography (AdS/CFT).
Fivebrane gravitational anomalies
International Nuclear Information System (INIS)
Becker, Katrin; Becker, Melanie
2000-01-01
Freed, Harvey, Minasian and Moore (FHMM) have proposed a mechanism to cancel the gravitational anomaly of the M-theory fivebrane coming from diffeomorphisms acting on the normal bundle. This procedure is based on a modification of the conventional M-theory Chern-Simons term. We apply the FHMM mechanism in the ten-dimensional type IIA theory. We then analyze the relation to the anomaly cancellation mechanism for the type IIA fivebrane proposed by Witten
2+1 topological term, anyons and their possible application in high Tc superconductivity
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Zhu Chuanjie.
1990-01-01
I review pedagogically some aspects about the SO(3) non-linear σ-model and the topological Hopf term (or the abelian Chern-Simons term). I argue that the presence of the topological Chern-Simons term is irrelevant (for regular gauge field configurations). I also give a brief introduction to the ideal anyon gas approach to high T c superconductivity. (author). 18 refs
Instanton effects in ABJM theory from Fermi gas approach
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Hatsuda, Yasuyuki [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie; Tokyo Institute of Technology (Japan). Dept. of Physics; Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst.; Nagoya Univ. (Japan). Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics
2012-11-19
We study the instanton effects of the ABJM partition function using the Fermi gas formalism. We compute the exact values of the partition function at the Chern-Simons levels k=1, 2, 3, 4, 6 up to N=44, 20, 18, 16, 14 respectively, and extract non-perturbative corrections from these exact results. Fitting the resulting non-perturbative corrections by their expected forms from the Fermi gas, we determine unknown parameters in them. After separating the oscillating behavior of the grand potential, which originates in the periodicity of the grand partition function, and the worldsheet instanton contribution, which is computed from the topological string theory, we succeed in proposing an analytical expression for the leading D2-instanton correction. Just as the perturbative result, the instanton corrections to the partition function are expressed in terms of the Airy function.
Yang, Wei-Wei; Li, Lei; Zhao, Jing-Sheng; Liu, Xiao-Xiong; Deng, Jian-Bo; Tao, Xiao-Ma; Hu, Xian-Ru
2018-05-01
By doing calculations based on density functional theory, we predict that the two-dimensional anti-ferromagnetic (AFM) NiOsCl6 as a Chern insulator can realize the quantum anomalous Hall (QAH) effect. We investigate the magnetocrystalline anisotropy energies in different magnetic configurations and the Néel AFM configuration is proved to be ground state. When considering spin–orbit coupling (SOC), this layered material with spins perpendicular to the plane shows properties as a Chern insulator characterized by an inversion band structure and a nonzero Chern number. The nontrivial band gap is 37 meV and the Chern number C = ‑1, which are induced by a strong SOC and AFM order. With strong SOC, the NiOsCl6 system performs a continuous topological phase transition from the Chern insulator to the trivial insulator upon the increasing Coulomb repulsion U. The critical U c is indicated as 0.23 eV, at which the system is in a metallic phase with . Upon increasing U, the E g reduces linearly with C = ‑1 for 0 U c . At last we analysis the QAH properties and this continuous topological phase transition theoretically in a two-band model. This AFM Chern insulator NiOsCl6 proposes not only a promising way to realize the QAH effect, but also a new material to study the continuous topological phase transition.
L lines, C points and Chern numbers: understanding band structure topology using polarization fields
Fösel, Thomas; Peano, Vittorio; Marquardt, Florian
2017-11-01
Topology has appeared in different physical contexts. The most prominent application is topologically protected edge transport in condensed matter physics. The Chern number, the topological invariant of gapped Bloch Hamiltonians, is an important quantity in this field. Another example of topology, in polarization physics, are polarization singularities, called L lines and C points. By establishing a connection between these two theories, we develop a novel technique to visualize and potentially measure the Chern number: it can be expressed either as the winding of the polarization azimuth along L lines in reciprocal space, or in terms of the handedness and the index of the C points. For mechanical systems, this is directly connected to the visible motion patterns.
Instanton bound states in ABJM theory
Energy Technology Data Exchange (ETDEWEB)
Hatsuda, Yasuyuki [DESY Hamburg (Germany). Theory Group; Tokyo Institute of Technology (Japan). Dept. of Physics; Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst. and Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics
2013-06-15
The partition function of the ABJM theory receives non-perturbative corrections due to instanton effects. We study these non-perturbative corrections, including bound states of worldsheet instantons and membrane instantons, in the Fermi-gas approach. We require that the total non-perturbative correction should be always finite for arbitrary Chern-Simons level. This finiteness is realized quite non-trivially because each bound state contribution naively diverges at some levels. The poles of each contribution should be canceled out in total. We use this pole cancellation mechanism to find unknown bound state corrections from known ones. We conjecture a general expression of the bound state contribution. Summing up all the bound state contributions, we find that the effect of bound states is simply incorporated into the worldsheet instanton correction by a redefinition of the chemical potential in the Fermi-gas system. Analytic expressions of the 3- and 4-membrane instanton corrections are also proposed.
International Nuclear Information System (INIS)
Bertrand, Bruno; Govaerts, Jan
2007-01-01
Abelian topologically massive gauge theories (TMGT) provide a topological mechanism to generate mass for a bosonic p-tensor field in any spacetime dimension. These theories include the (2+1)-dimensional Maxwell-Chern-Simons and (3+1)-dimensional Cremmer-Scherk actions as particular cases. Within the Hamiltonian formulation, the embedded topological field theory (TFT) sector related to the topological mass term is not manifest in the original phase space. However, through an appropriate canonical transformation, a gauge-invariant factorization of phase space into two orthogonal sectors is feasible. The first of these sectors includes canonically conjugate gauge-invariant variables with free massive excitations. The second sector, which decouples from the total Hamiltonian, is equivalent to the phase-space description of the associated non-dynamical pure TFT. Within canonical quantization, a likewise factorization of quantum states thus arises for the full spectrum of TMGT in any dimension. This new factorization scheme also enables a definition of the usual projection from TMGT onto topological quantum field theories in a most natural and transparent way. None of these results rely on any gauge-fixing procedure whatsoever
The Life and Work of Marvin Kenneth Simon
Alouini, Mohamed-Slim; Biglieri, Ezio; Divsalar, Dariush; Dolinar, Samuel; Goldsmith, Andrea J.; Milstein, Larry B.
2016-01-01
It is a measure of the importance and profundity of Marvin Kenneth Simon's contributions to communication theory that a tribute article and tutorial about his life and work is of current research relevance in spite of the continually accelerating
Relative entropy, mixed gauge-gravitational anomaly and causality
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Bhattacharyya, Arpan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Centre For High Energy Phsyics, Indian Institute of Science,560012 Bangalore (India); Cheng, Long [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Hung, Ling-Yan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Collaborative Innovation Center of Advanced Microstructures, Fudan University,220 Handan Road, 200433 Shanghai (China)
2016-07-25
In this note we explored the holographic relative entropy in the presence of the 5d Chern-Simons term, which introduces a mixed gauge-gravity anomaly to the dual CFT. The theory trivially satisfies an entanglement first law. However, to quadratic order in perturbations of the stress tensor T and current density J, there is a mixed contribution to the relative entropy bi-linear in T and J, signalling a potential violation of the positivity of the relative entropy. Miraculously, the term vanishes up to linear order in a derivative expansion. This prompted a closer inspection on a different consistency check, that involves time-delay of a graviton propagating in a charged background, scattered via a coupling supplied by the Chern-Simons term. The analysis suggests that the time-delay can take either sign, potentially violating causality for any finite value of the CS coupling.
Self-dual spin-3 and 4 theories
International Nuclear Information System (INIS)
Aragone, C.; Khoudeir, A.
1991-08-01
We present self-dual pure spin-3 and 4 actions using the physical relevant Dreibein fields. Since these actions start with a Chern-Simons like kinetic term (and therefore cannot be obtained through dimensional reduction) one might wonder whether they need the presence of auxiliary, ghost-killing fields. It turns out that they must contain, also in this three dimensional case, auxiliary fields. Auxiliary scalars do not break self-duality; their free action does not contain kinetic terms. (author). 12 refs
Topological Higgs mechanism with ordinary Higgs mechanism
International Nuclear Information System (INIS)
Oda Ichiro; Yahikozawa Shigeaki.
1989-12-01
Topological Higgs mechanism in higher dimensions is analyzed when ordinary Higgs potential exists. It is shown that if one-form B-field becomes massive by the ordinary Higgs mechanism, another D-2 form C-field also becomes massive through topological term in addition to the topological mass generation by the topological Higgs mechanism. Moreover we investigate this mechanism in three dimensional theories, that is to say, Chern-Simons theory and more general theory. (author). 10 refs
General solution of linear vector supersymmetry
International Nuclear Information System (INIS)
Blasi, Alberto; Maggiore, Nicola
2007-01-01
We give the general solution of the Ward identity for the linear vector supersymmetry which characterizes all topological models. Such a solution, whose expression is quite compact and simple, greatly simplifies the study of theories displaying a supersymmetric algebraic structure, reducing to a few lines the proof of their possible finiteness. In particular, the cohomology technology, usually involved for the quantum extension of these theories, is completely bypassed. The case of Chern-Simons theory is taken as an example
Magnus forces and statistics in 2 + 1 dimensions
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Davis, R.L.
1990-01-01
Spinning vortex solutions to the abelian Higgs model, not Nielsen-Olesen solutions, are appropriate to a Ginzburg-Landau description of superconductivity. The main physical distinction is that spinning vortices experience the Magnus force while Nielsen-Olesen vortices do not. In 2 + 1 dimensional superconductivity without a Chern-Simons interaction, the effect of the Magnus force is equivalent to that of a background fictitious magnetic field. Moreover, the phase obtained an interchanging two quasi-particles is always path-dependent. When a Chern-Simons term is added there is an additional localized Magnus flux at the vortex. For point-like vortices, the Chern-Simons interaction can be seen as defining their intrinsic statistics, but in realistic cases of vortices with finite size in strong Magnus fields the quasi-particle statistics are not well-defined
Chern–Simons dilaton black holes in 2 + 1 dimensions
International Nuclear Information System (INIS)
Moussa, Karim Ait; Clément, Gérard; Guennoune, Hakim
2016-01-01
We construct rotating magnetic solutions to the three-dimensional Einstein–Maxwell–Chern–Simons-dilaton theory with a Liouville potential. These include a class of black hole solutions which generalize the warped AdS black holes. The regular black holes belong to two disjointed sectors. The first sector includes black holes which have a positive mass and are co-rotating, while the black holes of the second sector have a negative mass and are counter-rotating. We also show that a particular, non-black hole, subfamily of our three-dimensional solutions may be uplifted to new regular non-asymptotically flat solutions of five-dimensional Einstein–Maxwell–Chern–Simons theory. (paper)
Misra, A
2002-01-01
Following the work on the exact evaluation of the non-perturbative contribution to the superpotential from open-membrane instanton in Heterotic M-theory, we evaluate systematically the contribution to the superpotential of a membrane instanton obtained by wrapping of a single M2-brane, once, on an isolated supersymmetric 3-cycle in a G sub 2 -holonomy manifold. We then try to relate the results obtained to those sketched out. We also do a heat-kernel asymptotics analysis to see whether one gets similar UV-divergent terms for (one or both of) the bosonic and fermionic determinants indicative of (partial) cancellation among them. The answer is in the affirmative, as expected by the supersymmetry of the starting membrane action. This work is a first step, both, in extending the work to the evaluation of non-perturbative superpotentials for non-rigid supersymmetric 3-cycle wrappings, and in understanding the large-N Chern-Simons/closed type-A topological string theory duality from M-theory point of view.
Localization on AdS{sub 2}×S{sup 1}
Energy Technology Data Exchange (ETDEWEB)
David, Justin R. [Centre for High Energy Physics, Indian Institute of Science,C.V. Raman Avenue, Bangalore, 560012 (India); Gava, Edi [INFN, Sezione di Trieste,Strada Costiera 11, Trieste (Italy); Gupta, Rajesh Kumar; Narain, Kumar [ICTP,Strada Costiera 11, Trieste, 34151 (Italy)
2017-03-09
Conformal symmetry relates the metric on AdS{sub 2}×S{sup 1} to that of S{sup 3}. This implies that under a suitable choice of boundary conditions for fields on AdS{sub 2} the partition function of conformal field theories on these spaces must agree which makes AdS{sub 2}×S{sup 1} a good testing ground to study localization on non-compact spaces. We study supersymmetry on AdS{sub 2}×S{sup 1} and determine the localizing Lagrangian for N=2 supersymmetric Chern-Simons theory on AdS{sub 2}×S{sup 1}. We evaluate the partition function of N=2 supersymmetric Chern-Simons theory on AdS{sub 2}×S{sup 1} using localization, where the radius of S{sup 1} is q times that of AdS{sub 2}. With boundary conditions on AdS{sub 2}×S{sup 1} which ensure that all the physical fields are normalizable and lie in the space of square integrable wave functions in AdS{sub 2}, the result for the partition function precisely agrees with that of the theory on the q-fold covering of S{sup 3}.
Wide gap Chern Mott insulating phases achieved by design
Guo, Hongli; Gangopadhyay, Shruba; Köksal, Okan; Pentcheva, Rossitza; Pickett, Warren E.
2017-12-01
Quantum anomalous Hall insulators, which display robust boundary charge and spin currents categorized in terms of a bulk topological invariant known as the Chern number (Thouless et al Phys. Rev. Lett. 49, 405-408 (1982)), provide the quantum Hall anomalous effect without an applied magnetic field. Chern insulators are attracting interest both as a novel electronic phase and for their novel and potentially useful boundary charge and spin currents. Honeycomb lattice systems such as we discuss here, occupied by heavy transition-metal ions, have been proposed as Chern insulators, but finding a concrete example has been challenging due to an assortment of broken symmetry phases that thwart the topological character. Building on accumulated knowledge of the behavior of the 3d series, we tune spin-orbit and interaction strength together with strain to design two Chern insulator systems with bandgaps up to 130 meV and Chern numbers C = -1 and C = 2. We find, in this class, that a trade-off between larger spin-orbit coupling and strong interactions leads to a larger gap, whereas the stronger spin-orbit coupling correlates with the larger magnitude of the Hall conductivity. Symmetry lowering in the course of structural relaxation hampers obtaining quantum anomalous Hall character, as pointed out previously; there is only mild structural symmetry breaking of the bilayer in these robust Chern phases. Recent growth of insulating, magnetic phases in closely related materials with this orientation supports the likelihood that synthesis and exploitation will follow.
Counterterms and dual holographic anomalies in CS gravity
Energy Technology Data Exchange (ETDEWEB)
Banados, Maximo [Departamento de Fisica, P. Universidad Catolica de Chile, Casilla 306, Santiago 22, Chile (Chile); Olea, Rodrigo [Departamento de Fisica, P. Universidad Catolica de Chile, Casilla 306, Santiago 22, Chile (Chile); Theisen, Stefan [Max-Planck-Institut fuer Gravitationphysik, Albert-Einstein-Institut, 14476 Golm (Germany)
2005-10-15
The holographic Weyl anomaly associated to Chern-Simons gravity in 2n+1 dimensions is proportional to the Euler term in 2n dimensions, with no contributions from the Weyl tensor. We compute the holographic energy-momentum tensor associated to Chern-Simons gravity directly from the action, in an arbitrary odd-dimensional spacetime. We show, in particular, that the counterterms rendering the action finite contain only terms of the Lovelock type.
Vacuum static compactified wormholes in eight-dimensional Lovelock theory
International Nuclear Information System (INIS)
Canfora, Fabrizio; Giacomini, Alex
2008-01-01
In this paper, new exact solutions in eight-dimensional Lovelock theory will be presented. These solutions are the vacuum static wormhole, the black hole, and generalized Bertotti-Robinson space-times with nontrivial torsion. All of the solutions have a cross product structure of the type M 5 xΣ 3 , where M 5 is a five-dimensional manifold and Σ 3 a compact constant curvature manifold. The wormhole is the first example of a smooth vacuum static Lovelock wormhole which is neither Chern-Simons nor Born-Infeld. It will be also discussed how the presence of torsion affects the 'navigableness' of the wormhole for scalar and spinning particles. It will be shown that the wormhole with torsion may act as 'geometrical filter': A very large torsion may 'increase the traversability' for scalars while acting as a 'polarizator' on spinning particles. This may have interesting phenomenological consequences.
Theory of activated transport in bilayer quantum Hall systems.
Roostaei, B; Mullen, K J; Fertig, H A; Simon, S H
2008-07-25
We analyze the transport properties of bilayer quantum Hall systems at total filling factor nu=1 in drag geometries as a function of interlayer bias, in the limit where the disorder is sufficiently strong to unbind meron-antimeron pairs, the charged topological defects of the system. We compute the typical energy barrier for these objects to cross incompressible regions within the disordered system using a Hartree-Fock approach, and show how this leads to multiple activation energies when the system is biased. We then demonstrate using a bosonic Chern-Simons theory that in drag geometries current in a single layer directly leads to forces on only two of the four types of merons, inducing dissipation only in the drive layer. Dissipation in the drag layer results from interactions among the merons, resulting in very different temperature dependences for the drag and drive layers, in qualitative agreement with experiment.
Fractionary statistics and field theories in (2+1) dimensions
International Nuclear Information System (INIS)
Gomes, M.
1989-01-01
The existence of fractionary angular momentum and the exotic statistics in many dimensions are analysed. The soliton type excitations of non linear sigma model with 0(3) symmetry are considered. The parity breaking through mass term and the generation of Chern Simon term are discussed in three dimensional fermion model. It is shown that the symmetry breaking can be due to vacuum and this possibility is illustrated in the context of Gross-Never similar model. (M.C.K.)
Improved Integral Attacks on SIMON32 and SIMON48 with Dynamic Key-Guessing Techniques
Directory of Open Access Journals (Sweden)
Zhihui Chu
2018-01-01
Full Text Available Dynamic key-guessing techniques, which exploit the property of AND operation, could improve the differential and linear cryptanalytic results by reducing the number of guessed subkey bits and lead to good cryptanalytic results for SIMON. They have only been applied in differential and linear attacks as far as we know. In this paper, dynamic key-guessing techniques are first introduced in integral cryptanalysis. According to the features of integral cryptanalysis, we extend dynamic key-guessing techniques and get better integral cryptanalysis results than before. As a result, we present integral attacks on 24-round SIMON32, 24-round SIMON48/72, and 25-round SIMON48/96. In terms of the number of attacked rounds, our attack on SIMON32 is better than any previously known attacks, and our attacks on SIMON48 are the same as the best attacks.
Entanglement entropy and higher spin holography in AdS{sub 3}
Energy Technology Data Exchange (ETDEWEB)
Boer, Jan de; Jottar, Juan I. [Institute for Theoretical Physics, University of Amsterdam,Science Park 904, Postbus 94485, 1090 GL Amsterdam (Netherlands)
2014-04-14
A holographic correspondence has been recently developed between higher spin theories in three-dimensional anti-de Sitter space (AdS{sub 3}) and two-dimensional Conformal Field Theories (CFTs) with extended symmetries. A class of such dualities involves SL(N,R)×SL(N,R) Chern-Simons gauge theories in the (2+1)-dimensional bulk spacetime, and CFTs with W{sub N} symmetry algebras on the (1+1)-dimensional boundary. The topological character of the bulk theory forces one to reconsider standard geometric notions such as black hole horizons and entropy, as well as the usual holographic dictionary. Motivated by this challenge, in this note we present a proposal to compute entanglement entropy in the W{sub N} CFTs via holographic methods. In particular, we introduce a functional constructed from Wilson lines in the bulk Chern-Simons theory that captures the entanglement entropy in the CFTs dual to standard AdS{sub 3} gravity, corresponding to SL(2,R)×SL(2,R) gauge group, and admits an immediate generalization to the higher spin case. We explicitly evaluate this functional for several known solutions of the bulk theory, including charged black holes dual to thermal CFT states carrying higher spin charge, and show that it reproduces expected features of entanglement entropy, study whether it obeys strong subadditivity, and moreover show that it reduces to the thermal entropy in the appropriate limit.
Aspects of defects in 3d-3d correspondence
International Nuclear Information System (INIS)
Gang, Dongmin; Kim, Nakwoo; Romo, Mauricio; Yamazaki, Masahito
2016-01-01
In this paper we study supersymmetric co-dimension 2 and 4 defects in the compactification of the 6d (2,0) theory of type A_N_−_1 on a 3-manifold M. The so-called 3d-3d correspondence is a relation between complexified Chern-Simons theory (with gauge group SL(N,ℂ)) on M and a 3d N=2 theory T_N[M]. We study this correspondence in the presence of supersymmetric defects, which are knots/links inside the 3-manifold. Our study employs a number of different methods: state-integral models for complex Chern-Simons theory, cluster algebra techniques, domain wall theory T[SU(N)], 5d N=2 SYM, and also supergravity analysis through holography. These methods are complementary and we find agreement between them. In some cases the results lead to highly non-trivial predictions on the partition function. Our discussion includes a general expression for the cluster partition function, which can be used to compute in the presence of maximal and certain class of non-maximal punctures when N>2. We also highlight the non-Abelian description of the 3d N=2T_N[M] theory with defect included, when such a description is available. This paper is a companion to our shorter paper http://dx.doi.org/10.1088/1751-8113/49/30/30LT02, which summarizes our main results.
Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c=1 Matrix Models
Pasquetti, Sara
2010-01-01
We address the nonperturbative structure of topological strings and c=1 matrix models, focusing on understanding the nature of instanton effects alongside with exploring their relation to the large-order behavior of the 1/N expansion. We consider the Gaussian, Penner and Chern-Simons matrix models, together with their holographic duals, the c=1 minimal string at self-dual radius and topological string theory on the resolved conifold. We employ Borel analysis to obtain the exact all-loop multi-instanton corrections to the free energies of the aforementioned models, and show that the leading poles in the Borel plane control the large-order behavior of perturbation theory. We understand the nonperturbative effects in terms of the Schwinger effect and provide a semiclassical picture in terms of eigenvalue tunneling between critical points of the multi-sheeted matrix model effective potentials. In particular, we relate instantons to Stokes phenomena via a hyperasymptotic analysis, providing a smoothing of the nonp...
The Simon and Simon-Mars tensors for stationary Einstein-Maxwell fields
International Nuclear Information System (INIS)
Bini, Donato; Cherubini, Christian; Jantzen, Robert T; Miniutti, Giovanni
2004-01-01
Modulo conventional scale factors, the Simon and Simon-Mars tensors are defined for stationary vacuum spacetimes so that their equality follows from the Bianchi identities of the second kind. In the nonvacuum case one can absorb additional source terms into a redefinition of the Simon tensor so that this equality is maintained. Among the electrovacuum class of solutions of the Einstein-Maxwell equations, the expression for the Simon tensor in the Kerr-Newman-Taub-NUT spacetime in terms of the Ernst potential is formally the same as in the vacuum case (modulo a scale factor), and its vanishing guarantees the simultaneous alignment of the principal null directions of the Weyl tensor, the Papapetrou field associated with the timelike Killing vector field, the electromagnetic field of the spacetime and even the Killing-Yano tensor
Yang, Chen Ning
2013-05-01
I do not remember whether I had met Prof. S. S. Chern when he was a graduate student of Tsinghua University in Peking (now Beijing) where my father was a mathematics professor, and I was in elementary school. But I do remember how I had met Mrs. Chern for the first time, in early October, 1929, when I was seven years old and she was in junior high school. Her father, Professor Tsen, had been a professor of Mathematics at Tsinghua University already for a number of years, and the Yangs were new comers that fall. The Tsens invited us to their house for dinner and that was when I first made the acquaintence of "big sister Tsen"...
Improved Linear Cryptanalysis of Reduced-Round SIMON-32 and SIMON-48
DEFF Research Database (Denmark)
Abdelraheem, Mohamed Ahmed; Alizadeh, Javad; Alkhzaimi, Hoda A.
2015-01-01
In this paper we analyse two variants of SIMON family of light-weight block ciphers against variants of linear cryptanalysis and present the best linear cryptanalytic results on these variants of reducedround SIMON to date. We propose a time-memory trade-off method that finds differential/ linear...
Effective gravitational wave stress-energy tensor in alternative theories of gravity
International Nuclear Information System (INIS)
Stein, Leo C.; Yunes, Nicolas
2011-01-01
The inspiral of binary systems in vacuum is controlled by the stress-energy of gravitational radiation and any other propagating degrees of freedom. For gravitational waves, the dominant contribution is characterized by an effective stress-energy tensor at future null infinity. We employ perturbation theory and the short-wavelength approximation to compute this stress-energy tensor in a wide class of alternative theories. We find that this tensor is generally a modification of that first computed by Isaacson, where the corrections can dominate over the general relativistic term. In a wide class of theories, however, these corrections identically vanish at asymptotically flat, future, null infinity, reducing the stress-energy tensor to Isaacson's. We exemplify this phenomenon by first considering dynamical Chern-Simons modified gravity, which corrects the action via a scalar field and the contraction of the Riemann tensor and its dual. We then consider a wide class of theories with dynamical scalar fields coupled to higher-order curvature invariants and show that the gravitational wave stress-energy tensor still reduces to Isaacson's. The calculations presented in this paper are crucial to perform systematic tests of such modified gravity theories through the orbital decay of binary pulsars or through gravitational wave observations.
Explicitly broken supersymmetry with exactly massless moduli
Energy Technology Data Exchange (ETDEWEB)
Dong, Xi [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States); Freedman, Daniel Z. [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States); Center for Theoretical Physics and Department of Mathematics,Massachusetts Institute of Technology,Cambridge, MA 02139 (United States); Zhao, Yue [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States)
2016-06-16
The AdS/CFT correspondence is applied to an analogue of the little hierarchy problem in three-dimensional supersymmetric theories. The bulk is governed by a supergravity theory in which a U(1) × U(1) R-symmetry is gauged by Chern-Simons fields. The bulk theory is deformed by a boundary term quadratic in the gauge fields. It breaks SUSY completely and sources an exactly marginal operator in the dual CFT. SUSY breaking is communicated by gauge interactions to bulk scalar fields and their spinor superpartners. The bulk-to-boundary propagator of the Chern-Simons fields is a total derivative with respect to the bulk coordinates. Integration by parts and the Ward identity permit evaluation of SUSY breaking effects to all orders in the strength of the deformation. The R-charges of scalars and spinors differ so large SUSY breaking mass shifts are generated. Masses of R-neutral particles such as scalar moduli are not shifted to any order in the deformation strength, despite the fact that they may couple to R-charged fields running in loops. We also obtain a universal deformation formula for correlation functions under an exactly marginal deformation by a product of holomorphic and anti-holomorphic U(1) currents.
Topological terms induced by finite temperature and density fluctuations
International Nuclear Information System (INIS)
Niemi, A.J.; Department of Physics, The Ohio State University, Columbus, Ohio 43210)
1986-01-01
In (3+1)-dimensional finite-temperature and -density SU(2) gauge theories with left-handed fermions, the three-dimensional Chern-Simons term (topological mass) can be induced by radiative corrections. This result is derived by use of a family's index theorem which also implies that in many other quantum field theories various additional lower-dimensional topological terms can be induced. In the high-temperature limit these terms dominate the partition function, which suggests applications to early-Universe cosmology
Heukelom, F.
2007-01-01
This paper provides an overview of the work of Herbert Simon and his ideas about rational decision making. By his own standards, Simon is an economist who works in the tradition of Adam Smith and Alfred Marshall. The central theme in Simon’s research is how human beings organize themselves in
Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity
Directory of Open Access Journals (Sweden)
Jacobo Diaz-Polo
2012-08-01
Full Text Available We review the black hole entropy calculation in the framework of Loop Quantum Gravity based on the quasi-local definition of a black hole encoded in the isolated horizon formalism. We show, by means of the covariant phase space framework, the appearance in the conserved symplectic structure of a boundary term corresponding to a Chern-Simons theory on the horizon and present its quantization both in the U(1 gauge fixed version and in the fully SU(2 invariant one. We then describe the boundary degrees of freedom counting techniques developed for an infinite value of the Chern-Simons level case and, less rigorously, for the case of a finite value. This allows us to perform a comparison between the U(1 and SU(2 approaches and provide a state of the art analysis of their common features and different implications for the entropy calculations. In particular, we comment on different points of view regarding the nature of the horizon degrees of freedom and the role played by the Barbero-Immirzi parameter. We conclude by presenting some of the most recent results concerning possible observational tests for theory.
First and second order vortex dynamics
International Nuclear Information System (INIS)
Kim, Yoonbai; Lee, Kimyeong
2002-01-01
The low energy dynamics of vortices in self-dual Abelian Higgs theory in (2+1)-dimensional spacetime is of second order in vortex velocity and characterized by the moduli space metric. When the Chern-Simons term with a small coefficient is added to the theory, we show that a term linear in vortex velocity appears and can be consistently added to the second order expression. We provide an additional check of the first and second order terms by studying the angular momentum in field theory
Rank of quantized universal enveloping algebras and modular functions
International Nuclear Information System (INIS)
Majid, S.; Soibelman, Ya.S.
1991-01-01
We compute an intrinsic rank invariant for quasitriangular Hopf algebras in the case of general quantum groups U q (g). As a function of q the rank has remarkable number theoretic properties connected with modular covariance and Galois theory. A number of examples are treated in detail, including rank (U q (su(3)) and rank (U q (e 8 )). We briefly indicate a physical interpretation as relating Chern-Simons theory with the theory of a quantum particle confined to an alcove of g. (orig.)
Erratum: Erratum to: "A higher-spin Chern-Simons theory of anyons"
Boulanger, N.; Sundell, P.; Valenzuela, M.
2017-09-01
In the published version there is an error in the affiliation (the word "Andre's" with accent) of the author Per Sundell. The present form in this erratum is the correct (should be the word "Andres" without accent). The affiliation under the symbol " b" should read: Departamento de Ciencias Físicas, Universidad Andres Bello, Santiago, Chile
Wang, Juven C; Gu, Zheng-Cheng; Wen, Xiao-Gang
2015-01-23
The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs. We find new examples of mixed gauge-gravity actions for U(1) SPTs in (4+1)D via the gravitational Chern-Simons term. Field theory representations of SPT invariants not only serve as tools for classifying SPTs, but also guide us in designing physical probes for them. In addition, our field theory representations are independently powerful for studying group cohomology within the mathematical context.
International Nuclear Information System (INIS)
Verlinde, Herman; Wang, L-T; Yavin, Itay; Wijnholt, Martijn
2008-01-01
We exhibit a simple and robust mechanism for bulk mediation of supersymmetry breaking between hidden and visible sectors localized on geometrically separated D-branes in type II string theory. The mediation proceeds via RR p-forms that couple via linear Chern-Simons terms to the abelian vector bosons on the branes. From a 4-d low energy perspective, the mechanism reduces to U(1) mediation
Topics in 2 + 1 and 3 + 1 dimensional physics
International Nuclear Information System (INIS)
Camperi, M.F.
1994-01-01
This thesis is concerned with the study of two different topics pertaining to two different dimensionalities in Field Theory. First, the issues Chern-Simons Gauge Field Theory in 2 + 1 dimensions, mainly as a field theoretic description of knots and links in three euclidean dimensions is addressed. The author provides both a non-perturbative and a perturbative approach, relating them in the large-N limit. A non-perturbative duality was found between the SU(N) k Chern-Simons theory and the SU(k) N one, providing a possible physical consequences of these constructions, notably the case of Fractional Statistics. Second, this thesis addresses the study of the so-called open-quotes vector modelclose quotes, written in the language of Chiral Perturbation Theory in the physical (3 + 1)-dimensional space time. This model was introduced as a possible way to study the physics of vector and pseudoscalar mesons and is based on the assumption that there is a limit of QCD where the vector mesons become massless. The author relates this model to the Hidden Symmetry Scheme, a model sharing the motivation with the previous one, but based on different assumptions. Considering only well established physical results as vector meson dominance, The thesis concludes that the vector model does not appear to be a good candidate for the effective description of vector mesons
Strings on AdS2 and the high-energy limit of noncritical M-theory
International Nuclear Information System (INIS)
Horava, Petr; Horava, Petr; Keeler, Cynthia A.
2007-01-01
Noncritical M-theory in 2+1 dimensions has been defined as a double-scaling limit of a nonrelativistic Fermi liquid on a flat two-dimensional plane. Here we study this noncritical M-theory in the limit of high energies, analogous to the alpha(prime) → ∞ limit of string theory. In the related case of two-dimensional Type 0A strings, it has been argued that the conformal alpha(prime) → ∞ limit leads to AdS 2 with a propagating fermion whose mass is set by the value of the RR flux. Here we provide evidence that in the high-energy limit, the natural ground state of noncritical M-theory similarly describes the AdS 2 x S 1 spacetime, with a massless propagating fermion. We argue that the spacetime effective theory in this background is captured by a topological higher-spin extension of conformal Chern-Simons gravity in 2+1 dimensions, consistently coupled to a massless Dirac field. Intriguingly, the two-dimensional plane populated by the original nonrelativistic fermions is essentially the twistor space associated with the symmetry group of the AdS 2 x S 1 spacetime; thus, at least in the high-energy limit, noncritical M-theory can be nonperturbatively described as a 'Fermi liquid on twistor space'
Kukk, Jaak, 1904-2001
1992-01-01
Aleksander Simon õppis veterinaariat, kuid ei lõpetanud, korporatsiooni astus kohe selle asutamisel ja Jaak Kukk oli tema akadeemiline kasuisa, kellele anti teada, et 1944. a Saksamaale rännanud A. Simon üritas 1946 salaja Rootsi põgeneda
High-temperature response functions and the non-Abelian Kubo formula
International Nuclear Information System (INIS)
Jackiw, R.; Nair, V.P.
1993-01-01
We describe the relationship between time-ordered and retarded response functions in a plasma. We obtain an expression, including the proper iε prescription, for the induced current due to hard thermal loops in a non-Abelian theory, thus giving the non-Abelian generalization of the Kubo formula. The result is closely related to the eikonal for a Chern-Simons theory and is relevant for a guage-invariant description of Landau damping in the quark-gluon plasma at high temperature
Factorized tree-level scattering in AdS4 x CP3
International Nuclear Information System (INIS)
Kalousios, Chrysostomos; Vergu, C.; Volovich, Anastasia
2009-01-01
AdS 4 /CFT 3 duality relating IIA string theory on AdS 4 x CP 3 to N = 6 superconformal Chern-Simons theory provides an arena for studying aspects of integrability in a new potentially exactly solvable system. In this paper we explore the tree-level worldsheet scattering for strings on AdS 4 x CP 3 . We compute all bosonic four-, five- and six-point amplitudes in the gauge-fixed action and demonstrate the absence of particle production.
Remarks on Fermion-Boson equivalence in three dimensions
International Nuclear Information System (INIS)
Dutra, A. de Souza; Natividade, C.P.
1998-06-01
Starting from a decomposition of the self-dual field in (2+1) dimensions, we build up an alternative quantum theory which consists of a self-dual model coupled to a Maxwell-generalized Chern-Simons theory. We discuss the fermion-boson equivalence of this quantum theory by comparing it to the Thirring model. Using these results we were able to compute the mass of the bosonized fermions up to third order in (1/m). Some problems related to the number of poles of the effective propagator are also addressed. (author)
International Nuclear Information System (INIS)
Mukhi, Sunil; Papageorgakis, Constantinos
2008-01-01
We examine the recently proposed ''3-algebra'' field theory for multiple M2-branes and show that when a scalar field valued in the 3-algebra develops a vacuum expectation value, the resulting Higgs mechanism has the novel effect of promoting topological (Chern-Simons) to dynamical (Yang-Mills) gauge fields. This leads to a precise derivation of the maximally supersymmetric Yang-Mills theory on multiple D2-branes and thereby provides a relationship between 3-algebras and Yang-Mills theories. We discuss the physical interpretation of this result.
Massive gravity with mass term in three dimensions
International Nuclear Information System (INIS)
Nakasone, Masashi; Oda, Ichiro
2009-01-01
We analyze the effect of the Pauli-Fierz mass term on a recently established, new massive gravity theory in three space-time dimensions. We show that the Pauli-Fierz mass term makes the new massive gravity theory nonunitary. Moreover, although we add the gravitational Chern-Simons term to this model, the situation remains unchanged and the theory stays nonunitary despite that the structure of the graviton propagator is greatly changed. Thus, the Pauli-Fierz mass term is not allowed to coexist with mass-generating higher-derivative terms in the new massive gravity.
Remarks on Fermion-Boson equivalence in three dimensions
Energy Technology Data Exchange (ETDEWEB)
Dutra, A de Souza [UNESP, Guaratingueta, SP (Brazil); Natividade, C P [Universidade Federal Fluminense, Niteroi, RJ (Brazil). Inst. de Fisica
1998-06-01
Starting from a decomposition of the self-dual field in (2+1) dimensions, we build up an alternative quantum theory which consists of a self-dual model coupled to a Maxwell-generalized Chern-Simons theory. We discuss the fermion-boson equivalence of this quantum theory by comparing it to the Thirring model. Using these results we were able to compute the mass of the bosonized fermions up to third order in (1/m). Some problems related to the number of poles of the effective propagator are also addressed. (author) 13 refs.
International Nuclear Information System (INIS)
Kogan, Y.I.
1989-05-01
Using the connection between (2+1) Chern-Simons gauge theory and 2d Conformal Field Theory the on-shell string condition is obtained as a condition of full independence of interior of (2+1) world. The new method for off-shell continuation is considered based on the introduction of the Maxwell term in (2+1) theory. This leads to dynamical transmutation of world-sheet dimensions - the off-shell string becomes topological membrane (topological means that (2+1) theory has topological mass term). The dependence of parameters of (2+1) theory under the external fields is discussed. (author). 17 refs
Hassett, Brendan; Tschinkel, Yuri
2017-01-01
Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems. There has been significant progress in this field with major new results, which have given new impetus to the study of rational curves and spaces of rational curves on K3 surfaces and their higher-dimensional generalizations. One main recent insight the book covers is the idea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces. The implementation of this idea led to proofs of long-standing conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new theorems in arithmetic. This proceedings volume covers these new insights in detail. .
The Life and Work of Marvin Kenneth Simon
Alouini, Mohamed-Slim
2016-12-30
It is a measure of the importance and profundity of Marvin Kenneth Simon\\'s contributions to communication theory that a tribute article and tutorial about his life and work is of current research relevance in spite of the continually accelerating rate of evolution in this area. Marv, as the entire community affectionately knew him, was one of the most prolific and influential communications researchers of his generation. Moreover, he laid the foundation for many of the techniques used in communication systems today. Marv\\'s death on September 23, 2007 continues to engender pangs not only of sadness at the passing of a great friend to many in our community, but also of regret that he is no longer with us to help in resolving the many challenges facing communication systems today.
On maximally supersymmetric Yang-Mills theories
International Nuclear Information System (INIS)
Movshev, M.; Schwarz, A.
2004-01-01
We consider ten-dimensional supersymmetric Yang-Mills theory (10D SUSY YM theory) and its dimensional reductions, in particular, BFSS and IKKT models. We formulate these theories using algebraic techniques based on application of differential graded Lie algebras and associative algebras as well as of more general objects, L ∞ - and A ∞ -algebras. We show that using pure spinor formulation of 10D SUSY YM theory equations of motion and isotwistor formalism one can interpret these equations as Maurer-Cartan equations for some differential Lie algebra. This statement can be used to write BV action functional of 10D SUSY YM theory in Chern-Simons form. The differential Lie algebra we constructed is closely related to differential associative algebra (Ω,∂) of (0,k)-forms on some supermanifold; the Lie algebra is tensor product of (Ω,) and matrix algebra. We construct several other algebras that are quasiisomorphic to (Ω,∂) and, therefore, also can be used to give BV formulation of 10D SUSY YM theory and its reductions. In particular, (Ω,∂) is quasiisomorphic to the algebra (B,d), constructed by Berkovits. The algebras (Ω 0 ,∂) and (B 0 ,d) obtained from (Ω,∂) and (B,d) by means of reduction to a point can be used to give a BV-formulation of IKKT model. We introduce associative algebra SYM as algebra where relations are defined as equations of motion of IKKT model and show that Koszul dual to the algebra (B 0 ,d) is quasiisomorphic to SYM
Probing Wilson loops in N=4 Chern–Simons-matter theories at weak coupling
Directory of Open Access Journals (Sweden)
Luca Griguolo
2016-02-01
Full Text Available For three-dimensional N=4 super-Chern–Simons-matter theories associated to necklace quivers U(N0×U(N1×⋯U(N2r−1, we study at quantum level the two kinds of 1/2 BPS Wilson loop operators recently introduced in arXiv:1506.07614. We perform a two-loop evaluation and find the same result for the two kinds of operators, so moving to higher loops a possible quantum uplift of the classical degeneracy. We also compute the 1/4 BPS bosonic Wilson loop and discuss the quantum version of the cohomological equivalence between fermionic and bosonic Wilson loops. We compare the perturbative result with the Matrix Model prediction and find perfect matching, after identification and remotion of a suitable framing factor. Finally, we discuss the potential appearance of three-loop contributions that might break the classical degeneracy and briefly analyze possible implications on the BPS nature of these operators.
International Nuclear Information System (INIS)
Canfora, Fabrizio; Giacomini, Alex; Troncoso, Ricardo
2008-01-01
Exact vacuum solutions with a nontrivial torsion for the Einstein-Gauss-Bonnet theory in five dimensions are constructed. We consider a class of static metrics whose spacelike section is a warped product of the real line with a nontrivial base manifold endowed with a fully antisymmetric torsion. It is shown that requiring solutions of this sort to exist, fixes the Gauss-Bonnet coupling such that the Lagrangian can be written as a Chern-Simons form. The metric describes black holes with an arbitrary, but fixed, base manifold. It is shown that requiring its ground state to possess unbroken supersymmetries fixes the base manifold to be locally a parallelized three-sphere. The ground state turns out to be half-BPS, which could not be achieved in the absence of torsion in vacuum. The Killing spinors are explicitly found
Chern Numbers Hiding in Time of Flight Images
Satija, Indubala; Zhao, Erhai; Ghosh, Parag; Bray-Ali, Noah
2011-03-01
Since the experimental realization of synthetic magnetic fields in neural ultracold atoms, transport measurement such as quantized Hall conductivity remains an open challenge. Here we propose a novel and feasible scheme to measure the topological invariants, namely the chern numbers, in the time of flight images. We study both the commensurate and the incommensurate flux, with the later being the main focus here. The central concept underlying our proposal is the mapping between the chern numbers and the size of the dimerized states that emerge when the two-dimensional hopping is tuned to the highly anisotropic limit. In a uncoupled double quantum Hall system exhibiting time reversal invariance, only odd-sized dimer correlation functions are non-zero and hence encode quantized spin current. Finally, we illustrate that inspite of highly fragmented spectrum, a finite set of chern numbers are meaningful. Our results are supported by direct numerical computation of transverse conductivity. NBA acknowledges support from a National Research Council postdoctoral research associateship.
Measuring the spin Chern number in time-reversal-invariant Hofstadter optical lattices
Energy Technology Data Exchange (ETDEWEB)
Zhang, Dan-Wei, E-mail: zdanwei@126.com [Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, SPTE, South China Normal University, Guangzhou 510006 (China); Cao, Shuai, E-mail: shuaicao2004@163.com [Department of Applied Physics, College of Electronic Engineering, South China Agricultural University, Guangzhou 510642 China (China)
2016-10-14
We propose an experimental scheme to directly measure the spin Chern number of the time-reversal-invariant Hofstadter model in optical lattices. We first show that this model can be realized by using ultracold Fermi atoms with two pseudo-spin states encoded by the internal Zeeman states in a square optical lattice and the corresponding topological Bloch bands are characterized by the spin Chern number. We then propose and numerically demonstrate that this topological invariant can be extracted from the shift of the hybrid Wannier center in the optical lattice. By spin-resolved in situ detection of the atomic densities along the transverse direction combined with time-of-flight measurement along another spatial direction, the spin Chern number in this system is directly measured. - Highlights: • The cold-atom optical-lattice scheme for realizing the time-reversal-invariant Hofstadter model is proposed. • The intrinsic spin Chern number related to the hybrid Wannier center in the optical lattice is investigated. • Direct measurement of the spin Chern number in the proposed system is theoretically demonstrated.
Topics in field theory-higher spins, CFT, and gravity
International Nuclear Information System (INIS)
Yang, Z.
1990-01-01
Several topics in field theory are investigated. (1) Massive higher spin actions are obtained as gauge theories from the dimensional reduction of the corresponding massless ones. (2) The author considers a model of spin4 and spin2 interaction through the Bel-Robinson tensor of spin2 field, which in conserved at free level. The coupling is inconsistent, yet there are indications that adding still higher spin couplings would be a promising direction to achieve consistency. (3) Energy and Stability of Einstein-Gauss-Bonnet models of gravity are studied. It is shown that flat space is stable while AdS is not. (4) Gauged Wess-Zumino-Witten models are studied in detail. The equivalence to GKO construction of conformal field theory is considered. BRST quantization of the models is given. (5) Nonrenormalizability of quantum gravity is, in the binomial first order metric formulation, traced to a mismatch between the symmetries of its quadratic and cubic term. (6) The possibility that the gravitational model defined in D = 3 by an action which is the sum of Einstein and Chern-Simons terms is a viable quantum theory is investigated. It is shown that it is compatible with power-counting renormalizability. Gauge invariant regularizations, however, have not been found to exist. Detailed BRS analysis shows that there are possible anomalies
Field theory of anyons and the fractional quantum Hall effect
International Nuclear Information System (INIS)
Viefers, S.F.
1997-11-01
The thesis is devoted to a theoretical study of anyons, i.e. particles with fractional statistics moving in two space dimensions, and the quantum Hall effect. The latter constitutes the only known experimental realization of anyons in that the quasiparticle excitations in the fractional quantum Hall system are believed to obey fractional statistics. First, the properties of ideal quantum gases in two dimensions and in particular the equation of state of the free anyons gas are discussed. Then, a field theory formulation of anyons in a strong magnetic field is presented and later extended to a system with several species of anyons. The relation of this model to fractional exclusion statistics, i.e. intermediate statistics introduced by a generalization of the Pauli principle, and to the low-energy excitations at the edge of the quantum Hall system is discussed. Finally, the Chern-Simons-Landau-Ginzburg theory of the fractional quantum Hall effect is studied, mainly focusing on edge effects; both the ground state and the low-energy edge excitations are examined in the simple one-component model and in an extended model which includes spin effects
Coupling-matrix approach to the Chern number calculation in disordered systems
International Nuclear Information System (INIS)
Zhang Yi-Fu; Ju Yan; Sheng Li; Shen Rui; Xing Ding-Yu; Yang Yun-You; Sheng Dong-Ning
2013-01-01
The Chern number is often used to distinguish different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite crystalline and disordered systems. To show its effectiveness, we apply the approach to the Haldane model and the lattice Hofstadter model, and obtain the correct quantized Chern numbers. The disorder-induced topological phase transition is well reproduced, when the disorder strength is increased beyond the critical value. We expect the method to be widely applicable to the study of topological quantum numbers. (rapid communication)
Geometric Lagrangian approach to the physical degree of freedom count in field theory
Díaz, Bogar; Montesinos, Merced
2018-05-01
To circumvent some technical difficulties faced by the geometric Lagrangian approach to the physical degree of freedom count presented in the work of Díaz, Higuita, and Montesinos [J. Math. Phys. 55, 122901 (2014)] that prevent its direct implementation to field theory, in this paper, we slightly modify the geometric Lagrangian approach in such a way that its resulting version works perfectly for field theory (and for particle systems, of course). As in previous work, the current approach also allows us to directly get the Lagrangian constraints, a new Lagrangian formula for the counting of the number of physical degrees of freedom, the gauge transformations, and the number of first- and second-class constraints for any action principle based on a Lagrangian depending on the fields and their first derivatives without performing any Dirac's canonical analysis. An advantage of this approach over the previous work is that it also allows us to handle the reducibility of the constraints and to get the off-shell gauge transformations. The theoretical framework is illustrated in 3-dimensional generalized general relativity (Palatini and Witten's exotic actions), Chern-Simons theory, 4-dimensional BF theory, and 4-dimensional general relativity given by Palatini's action with a cosmological constant.
On matrix-model approach to simplified Khovanov-Rozansky calculus
Morozov, A.; Morozov, And.; Popolitov, A.
2015-10-01
Wilson-loop averages in Chern-Simons theory (HOMFLY polynomials) can be evaluated in different ways - the most difficult, but most interesting of them is the hypercube calculus, the only one applicable to virtual knots and used also for categorification (higher-dimensional extension) of the theory. We continue the study of quantum dimensions, associated with hypercube vertices, in the drastically simplified version of this approach to knot polynomials. At q = 1 the problem is reformulated in terms of fat (ribbon) graphs, where Seifert cycles play the role of vertices. Ward identities in associated matrix model provide a set of recursions between classical dimensions. For q ≠ 1 most of these relations are broken (i.e. deformed in a still uncontrollable way), and only few are protected by Reidemeister invariance of Chern-Simons theory. Still they are helpful for systematic evaluation of entire series of quantum dimensions, including negative ones, which are relevant for virtual link diagrams. To illustrate the effectiveness of developed formalism we derive explicit expressions for the 2-cabled HOMFLY of virtual trefoil and virtual 3.2 knot, which involve respectively 12 and 14 intersections - far beyond any dreams with alternative methods. As a more conceptual application, we describe a relation between the genus of fat graph and Turaev genus of original link diagram, which is currently the most effective tool for the search of thin knots.
International Nuclear Information System (INIS)
Yunes, Nicolas; O'Shaughnessy, Richard; Owen, Benjamin J.; Alexander, Stephon
2010-01-01
Gravitational parity violation is a possibility motivated by particle physics, string theory, and loop quantum gravity. One effect of it is amplitude birefringence of gravitational waves, whereby left and right circularly polarized waves propagate at the same speed but with different amplitude evolution. Here we propose a test of this effect through coincident observations of gravitational waves and short gamma-ray bursts from binary mergers involving neutron stars. Such gravitational waves are highly left or right circularly polarized due to the geometry of the merger. Using localization information from the gamma-ray burst, ground-based gravitational wave detectors can measure the distance to the source with reasonable accuracy. An electromagnetic determination of the redshift from an afterglow or host galaxy yields an independent measure of this distance. Gravitational parity violation would manifest itself as a discrepancy between these two distance measurements. We exemplify such a test by considering one specific effective theory that leads to such gravitational parity violation, Chern-Simons gravity. We show that the advanced LIGO-Virgo network and all-sky gamma-ray telescopes can be sensitive to the propagating sector of Chern-Simons gravitational parity violation to a level roughly 2 orders of magnitude better than current stationary constraints from the LAGEOS satellites.
Dissociating Simon and affordance compatibility effects: silhouettes and photographs.
Pappas, Zissis
2014-12-01
When a graspable object's handle is oriented to the same side as the response hand, responses are quicker and more accurate than when it is oriented to the opposite side. This effect has been attributed to the affordance of the object's handle (Tucker & Ellis, 1998). Recent findings suggest this effect results instead from an abstract spatial response code (i.e., Simon effect; Cho & Proctor, 2010). However, the stimuli used in these previous studies differ in the amount of object and environmental depth information they contain, which may be critical to conveying an affordance. This information could explain these disparate findings as well as dissociate Simon and affordance compatibility effects. Four experiments demonstrate that the Simon effect results from the absence of this information, as in a silhouette, and the affordance effect results from its presence, as in a photograph. A fifth experiment confirmed that modifying information associated with the affordance, rather than the modification itself, produced the effects observed in the previous experiments. These findings support the following: (a) the internal details of an object and environmental depth can dissociate Simon and affordance compatibility effects, (b) this information is necessary to convey the object's graspable affordance, and (c) the outer shape of the object is not sufficient to elicit an affordance effect. These findings are discussed in relation to the theory of embodied cognition. Copyright © 2014 Elsevier B.V. All rights reserved.
DEFF Research Database (Denmark)
Angella, Daniele; Calamai, Simone; Spotti, Cristiano
2017-01-01
We undertake the study of an analogue of the Yamabe problem for complex manifolds. More precisely, for any conformal Hermitian structure on a compact complex manifold, we are concerned in the existence of metrics with constant Chern scalar curvature. In this note, we set the problem and we provid...
On a canonical quantization of 3D Anti de Sitter pure gravity
Kim, Jihun; Porrati, Massimo
2015-10-01
We perform a canonical quantization of pure gravity on AdS 3 using as a technical tool its equivalence at the classical level with a Chern-Simons theory with gauge group SL(2,{R})× SL(2,{R}) . We first quantize the theory canonically on an asymptotically AdS space -which is topologically the real line times a Riemann surface with one connected boundary. Using the "constrain first" approach we reduce canonical quantization to quantization of orbits of the Virasoro group and Kähler quantization of Teichmüller space. After explicitly computing the Kähler form for the torus with one boundary component and after extending that result to higher genus, we recover known results, such as that wave functions of SL(2,{R}) Chern-Simons theory are conformal blocks. We find new restrictions on the Hilbert space of pure gravity by imposing invariance under large diffeomorphisms and normalizability of the wave function. The Hilbert space of pure gravity is shown to be the target space of Conformal Field Theories with continuous spectrum and a lower bound on operator dimensions. A projection defined by topology changing amplitudes in Euclidean gravity is proposed. It defines an invariant subspace that allows for a dual interpretation in terms of a Liouville CFT. Problems and features of the CFT dual are assessed and a new definition of the Hilbert space, exempt from those problems, is proposed in the case of highly-curved AdS 3.
On a canonical quantization of 3D Anti de Sitter pure gravity
Energy Technology Data Exchange (ETDEWEB)
Kim, Jihun [Center for Cosmology and Particle Physics, Department of Physics,New York University, 4 Washington Place, New York, NY 10003 (United States); Porrati, Massimo [Center for Cosmology and Particle Physics, Department of Physics,New York University, 4 Washington Place, New York, NY 10003 (United States); CERN PH-TH, CH 1211,Geneva 23 (Switzerland)
2015-10-14
We perform a canonical quantization of pure gravity on AdS{sub 3} using as a technical tool its equivalence at the classical level with a Chern-Simons theory with gauge group SL(2,ℝ)×SL(2,ℝ). We first quantize the theory canonically on an asymptotically AdS space –which is topologically the real line times a Riemann surface with one connected boundary. Using the “constrain first” approach we reduce canonical quantization to quantization of orbits of the Virasoro group and Kähler quantization of Teichmüller space. After explicitly computing the Kähler form for the torus with one boundary component and after extending that result to higher genus, we recover known results, such as that wave functions of SL(2,ℝ) Chern-Simons theory are conformal blocks. We find new restrictions on the Hilbert space of pure gravity by imposing invariance under large diffeomorphisms and normalizability of the wave function. The Hilbert space of pure gravity is shown to be the target space of Conformal Field Theories with continuous spectrum and a lower bound on operator dimensions. A projection defined by topology changing amplitudes in Euclidean gravity is proposed. It defines an invariant subspace that allows for a dual interpretation in terms of a Liouville CFT. Problems and features of the CFT dual are assessed and a new definition of the Hilbert space, exempt from those problems, is proposed in the case of highly-curved AdS{sub 3}.
Walcher, J.
2006-10-01
This book is a find. Mariño meets the challenge of filling in less than 200 pages the need for an accessible review of topological gauge / gravity duality. He is one of the pioneers of the subject and a clear expositor. It is no surprise that reading this book is a great pleasure. The existence of dualities between gauge theories and theories of gravity remains one of the most surprising recent discoveries in mathematical physics. While it is probably fair to say that we do not yet understand the full reach of such a relation, the impressive amount of evidence that has accumulated over the past years can be regarded as a substitute for a proof, and will certainly help to delineate the question of what is the most fundamental quantum mechanical theory. As has been the case in the past, it is in the context of Witten's 'topological' quantum theories that the mathematical framework is well enough established to firmly ground, and fully benefit from, the development of the physical theories. This book makes an important contribution to this new chapter in the math / physics interaction. There are two main instances of topological gauge/gravity duality. In the A-model, Chern Simons gauge theory on the 3-sphere is related to the closed topological string theory on the local Calabi Yau 3-fold {\\mathcal O}_{{\\mathbb P}^1}(-1) \\oplus{\\mathcal O}_{{\\mathbb P}^1} (-1), also known as the resolved conifold (Gopakumar-Vafa duality). In the B-model, certain types of matrix models are related on the gravity side to topological strings on certain cousins of the deformed conifold (Dijkgraaf-Vafa duality). In both cases, and similarly to the more physical AdS/CFT correspondence, the duality can be discovered by realizing the gauge theory as the target space theory of open strings ending on particular D-branes in a geometry closely related to the closed string background of the gravity theory. The A-branes supporting Chern Simons theory are wrapped on the Lagrangian three
Energy Technology Data Exchange (ETDEWEB)
Hoyler, Frieder [Fachhochschule Aachen, Juelich (Germany). Strahlenschutzkursstaette
2013-09-01
The CHERNE network is promoting the cooperation between colleges and research facilities at the training of students. The article describes particular study courses in the field of radiation protection. (orig.)
Orbifold matrix models and fuzzy extra dimensions
Chatzistavrakidis, Athanasios; Zoupanos, George
2011-01-01
We revisit an orbifold matrix model obtained as a restriction of the type IIB matrix model on a Z_3-invariant sector. An investigation of its moduli space of vacua is performed and issues related to chiral gauge theory and gravity are discussed. Modifications of the orbifolded model triggered by Chern-Simons or mass deformations are also analyzed. Certain vacua of the modified models exhibit higher-dimensional behaviour with internal geometries related to fuzzy spheres.
Canonical symmetry in a system with singular Lagrangian and ward identities
International Nuclear Information System (INIS)
Li Ziping
1994-01-01
An algorithm to construct the generator of gauge transformation for a constrained Hamiltonian system is given. The relationships among the coefficients connecting with first-class constraints in the generator is cleared. Based on the phase space generating function, the corresponding Ward identities in canonical formalism is deduced. The preliminary applications of above results to a model in field theory which is functionally equivalent to the mixed Chern-Simons Lagrangian is discussed in detail
Floris Heukelom
2007-01-01
This paper provides an overview of the work of Herbert Simon and his ideas about rational decision making. By his own standards, Simon is an economist who works in the tradition of Adam Smith and Alfred Marshall. The central theme in Simon’s research is how human beings organize themselves in different structures of distributed decision making in order to achieve a degree of rationality that is higher than which can be attained by the individual. In this realm his main preoccupation are hiera...
Holographic entanglement entropy for gravitational anomaly in four dimensions
Energy Technology Data Exchange (ETDEWEB)
Ali, Tibra [Perimeter Institute for Theoretical Physics, 31 Caroline Street N., Waterloo, ON N2L 2Y5 (Canada); Haque, S. Shajidul [Laboratory for Quantum Gravity & Strings, Department of Mathematics & Applied Mathematics,University of Cape Town, Mathematics Building, Rondebosch, Cape Town, 7700 (South Africa); Murugan, Jeff [Laboratory for Quantum Gravity & Strings, Department of Mathematics & Applied Mathematics,University of Cape Town, Mathematics Building, Rondebosch, Cape Town, 7700 (South Africa); School of Natural Sciences, Institute for Advanced Study,1 Einstein Dr., Princeton, NJ 08540 (United States)
2017-03-15
We compute the holographic entanglement entropy for the anomaly polynomial TrR{sup 2} in 3+1 dimensions. Using the perturbative method developed for computing entanglement entropy for quantum field theories, we also compute the parity odd contribution to the entanglement entropy of the dual field theory that comes from a background gravitational Chern-Simons term. We find that, in leading order in the perturbation of the background geometry, the two contributions match except for a logarithmic divergent term on the field theory side. We interpret this extra contribution as encoding our ignorance of the source which creates the perturbation of the geometry.
John F. Simon, jr. / John F. jun. Simon ; interv. Tilman Baumgärtel
Simon, John F. jun.
2006-01-01
Ameerika kunstnikust-programmeerijast Jon F. Simon juuniorist (sünd. 1963), tema loomingust, vestlus kunstnikuga 19. 12. 1999. a. tema ateljees. J. F. Simon jun.-i teosed on tarkvara. Monitoril tekkinud kujutisi on kunstnik eksponeerinud nimetuse "Panels" all. Kunstniku joonistusprogrammist, arvutiprogrammist "Every Icon", mis asub Internetis, tööst "Combination", võrgutööst "Alter Stars" (1995-1998) ja muust
On the spontaneous breakdown of massive gravities in 2 + 1 dimension
International Nuclear Information System (INIS)
Aragone, C.; Aria, P.J.; Andes Merida, Univ.; Khoudeir, A.
1997-01-01
This paper shows that locally Lorentz-invariant, third-order, topological massive gravity cannot be broken down either to the local diffeomorphism subgroup or to the rigid Poincare' group. On the other hand, the recently formulated, locally diffeomorphism-invariant, second order massive tradic (translational) Chern-Simons gravity breaks down on rigid Minkowski space to a double massive spin-two system. This flat double massive action is the uniform spin-two generalization of the Maxwell-Chern-Simons-Proca system which one is left with after U(1) Abelian gauge invariance breaks down in the presence of a sextic Higgs potential
Simon van der Meer (1925-2011)
2011-01-01
Simon van der Meer was a true giant of modern particle physics, though a gentle one. His contributions to accelerator science remain vital for the operation of accelerators such as the LHC today. Simon was an electrical engineer who grew up in The Hague, moving on to Delft University to study electrical engineering. After a short stint with Philips, he came to CERN in 1956, just two years after the lab opened, and remained with us until his retirement in 1990. Simon was an incredibly inventive man. When confronted with a problem, he would sink into deep reflection, rarely emerging until he had a solution. One of us, Steve Myers, remembers him as a man who did not suffer fools gladly, and who was extremely taciturn. Simon would never use two words where one would suffice. But that one word would invariably be the right one. Simon is best known for his contribution to the SPS collider project, for which he was awarded the Nobel Prize, jointly with Carlo Rubbia, in 1984. Stochastic cooling, the in...
Strong phase correlations of solitons of nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Litvak, A.G.; Mironov, V.A.; Protogenov, A.P.
1994-06-01
We discuss the possibility to suppress the collapse in the nonlinear 2+1 D Schroedinger equation by using the gauge theory of strong phase correlations. It is shown that invariance relative to q-deformed Hopf algebra with deformation parameter q being the fourth root of unity makes the values of the Chern-Simons term coefficient, k=2, and of the coupling constant, g=1/2, fixed; no collapsing solutions are present at those values. (author). 21 refs
Interference of Spin-2 Self-Dual Modes
Ilha, Anderson; Wotzasek, Clovis
2001-01-01
We study the effects of interference between the self-dual and anti self-dual massive modes of the linearized Einstein-Chern-Simons topological gravity. The dual models to be used in the interference process are carefully analyzed with special emphasis on their propagating spectrum. We identify the opposite dual aspects, necessary for the application of the interference formalism on this model. The soldered theory so obtained displays explicitly massive modes of the Proca type. It may also be...
Lorentz and CPT violation in QED revisited: A missing analysis
Energy Technology Data Exchange (ETDEWEB)
Del Cima, Oswaldo M., E-mail: wadodelcima@if.uff.b [Universidade Federal Fluminense (UFF), Polo Universitario de Rio das Ostras, Rua Recife s/n, 28890-000, Rio das Ostras, RJ (Brazil); Fonseca, Jakson M., E-mail: jakson.fonseca@ufv.b [Universidade Federal de Vicosa (UFV), Departamento de Fisica, Avenida Peter Henry Rolfs s/n, 36570-000, Vicosa, MG (Brazil); Franco, Daniel H.T., E-mail: daniel.franco@ufv.b [Universidade Federal de Vicosa (UFV), Departamento de Fisica, Avenida Peter Henry Rolfs s/n, 36570-000, Vicosa, MG (Brazil); Piguet, Olivier, E-mail: opiguet@pq.cnpq.b [Universidade Federal do Espirito Santo (UFES), Departamento de Fisica, Campus Universitario de Goiabeiras, 29060-900, Vitoria, ES (Brazil)
2010-05-03
We investigate the breakdown of Lorentz symmetry in QED by a CPT violating interaction term consisting of the coupling of an axial fermion current with a constant vector field b, in the framework of algebraic renormalization - a regularization-independent method. We show, to all orders in perturbation theory, that a CPT-odd and Lorentz violating Chern-Simons-like term, definitively, is not radiatively induced by the axial coupling of the fermions with the constant vector b.
Lorentz and CPT violation in QED revisited: A missing analysis
International Nuclear Information System (INIS)
Del Cima, Oswaldo M.; Fonseca, Jakson M.; Franco, Daniel H.T.; Piguet, Olivier
2010-01-01
We investigate the breakdown of Lorentz symmetry in QED by a CPT violating interaction term consisting of the coupling of an axial fermion current with a constant vector field b, in the framework of algebraic renormalization - a regularization-independent method. We show, to all orders in perturbation theory, that a CPT-odd and Lorentz violating Chern-Simons-like term, definitively, is not radiatively induced by the axial coupling of the fermions with the constant vector b.
Bardeen-anomaly and Wess-Zumino term in the supersymmetric standard model
Ferrara, Sergio; Porrati, Massimo; Stora, Raymond Félix
1994-01-01
We construct the Bardeen anomaly and its related Wess-Zumino term in the supersymmetric standard model. In particular we show that it can be written in terms of a composite linear superfield related to supersymmetrized Chern-Simons forms, in very much the same way as the Green-Schwarz term in four-dimensional string theory. Some physical applications, such as the contribution to the g-2 of gauginos when a heavy top is integrated out, are briefly discussed.
Notes on black holes and three dimensional gravity
International Nuclear Information System (INIS)
Banados, Maximo
1999-01-01
In these notes we review some relevant results on 2+1 quantum gravity. These include the Chern-Simons formulation and its affine Kac-Moody symmetry, the asymptotic algebra of Brown and Henneaux, and the statistical mechanics description of 2+1 black holes. A brief introduction to the classical and semiclassical aspects of black holes is also included. The level of the notes is basic assuming only some knowledge on Statistical Mechanics, General Relativity and Yang-Mills theory
Presheaves of symmetric tensor categories and nets of C*-algebras
Vasselli, Ezio
2012-01-01
Motivated by algebraic quantum field theory, we study presheaves of symmetric tensor categories defined over the base of a space, intended as a spacetime. Any section of a presheaf (that is, any "superselection sector", in the applications that we have in mind) defines a holonomy representation whose triviality is measured by Cheeger-Chern-Simons characteristic classes, and a non-abelian unitary cocycle defining a Lie group gerbe. We show that, given an embedding in a presheaf of full subcate...
Thermodynamics of higher spin black holes in AdS3
de Boer, Jan; Jottar, Juan I.
2014-01-01
We discuss the thermodynamics of recently constructed three-dimensional higher spin black holes in SL( N, ) × SL( N, ) Chern-Simons theory with generalized asymptotically-anti-de Sitter boundary conditions. From a holographic perspective, these bulk theories are dual to two-dimensional CFTs with WN symmetry algebras, and the black hole solutions are dual to thermal states with higher spin chemical potentials and charges turned on. Because the notion of horizon area is not gauge-invariant in the higher spin theory, the traditional approaches to the computation of black hole entropy must be reconsidered. One possibility, explored in the recent literature, involves demanding the existence of a partition function in the CFT, and consistency with the first law of thermodynamics. This approach is not free from ambiguities, however, and in particular different definitions of energy result in different expressions for the entropy. In the present work we show that there are natural definitions of the thermodynamically conjugate variables that follow from careful examination of the variational principle, and moreover agree with those obtained via canonical methods. Building on this intuition, we derive general expressions for the higher spin black hole entropy and free energy which are written entirely in terms of the Chern-Simons connections, and are valid for both static and rotating solutions. We compare our results to other proposals in the literature, and provide a new and efficient way to determine the generalization of the Cardy formula to a situation with higher spin charges.
Dynamical contents of unconventional supersymmetry
Energy Technology Data Exchange (ETDEWEB)
Guevara, Alfredo [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile); Departamento de Física, Universidad de Concepción,Casilla 160-C, Concepción (Chile); Pais, Pablo [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile); Physique Théorique et Mathématique,Université Libre de Bruxelles and International Solvay Institutes,Campus Plaine C.P. 231, B-1050 Bruxelles (Belgium); Zanelli, Jorge [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile)
2016-08-11
The Dirac Hamiltonian formalism is applied to a system in (2+1)-dimensions consisting of a Dirac field ψ minimally coupled to Chern-Simons U(1) and SO(2,1) connections, A and ω, respectively. This theory is connected to a supersymmetric Chern-Simons form in which the gravitino has been projected out (unconventional supersymmetry) and, in the case of a flat background, corresponds to the low energy limit of graphene. The separation between first-class and second-class constraints is performed explicitly, and both the field equations and gauge symmetries of the Lagrangian formalism are fully recovered. The degrees of freedom of the theory in generic sectors shows that the propagating states correspond to fermionic modes in the background determined by the geometry of the graphene sheet and the nondynamical electromagnetic field. This is shown for the following canonical sectors: i) a conformally invariant generic description where the spinor field and the dreibein are locally rescaled; ii) a specific configuration for the Dirac fermion consistent with its spin, where Weyl symmetry is exchanged by time reparametrizations; iii) the vacuum sector ψ=0, which is of interest for perturbation theory. For the latter the analysis is adapted to the case of manifolds with boundary, and the corresponding Dirac brackets together with the centrally extended charge algebra are found. Finally, the SU(2) generalization of the gauge group is briefly treated, yielding analogous conclusions for the degrees of freedom.
Characterizing the Hofstadter butterfly's outline with Chern numbers
International Nuclear Information System (INIS)
Goldman, N
2009-01-01
In this work, we report original properties inherent to independent particles subjected to a magnetic field by emphasizing the existence of regular structures in the energy spectrum's outline. We show that this fractal curve, the well-known Hofstadter butterfly's outline, is associated with a specific sequence of Chern numbers that correspond to the quantized transverse conductivity. Indeed the topological invariant that characterizes the fundamental energy band depicts successive stairways as the magnetic flux varies. Moreover each stairway is shown to be labelled by another Chern number which measures the charge transported under displacement of the periodic potential. We put forward the universal character of these properties by comparing the results obtained for the square and the honeycomb geometries.
Topological quantum field theory: 20 years later
DEFF Research Database (Denmark)
Reshetikhin, Nicolai
2008-01-01
This article is an overview of the developments in topological quantum ﬁeld theory, and, in particular on the progress in the Chern–Simons theory.......This article is an overview of the developments in topological quantum ﬁeld theory, and, in particular on the progress in the Chern–Simons theory....
Mixed symmetry tensors in the worldline formalism
Energy Technology Data Exchange (ETDEWEB)
Corradini, Olindo [Dipartimento di Scienze Fisiche, Informatiche e Matematiche,Università degli Studi di Modena e Reggio Emilia, via Campi 213/A, I-41125 Modena (Italy); INFN - Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy); Edwards, James P. [Department of Mathematical Sciences, University of Bath,Claverton Down, Bath BA2 7AY (United Kingdom)
2016-05-10
We consider the first quantised approach to quantum field theory coupled to a non-Abelian gauge field. Representing the colour degrees of freedom with a single family of auxiliary variables the matter field transforms in a reducible representation of the gauge group which — by adding a suitable Chern-Simons term to the particle action — can be projected onto a chosen fully (anti-)symmetric representation. By considering F families of auxiliary variables, we describe how to extend the model to arbitrary tensor products of F reducible representations, which realises a U(F) “flavour” symmetry on the worldline particle model. Gauging this symmetry allows the introduction of constraints on the Hilbert space of the colour fields which can be used to project onto an arbitrary irreducible representation, specified by a certain Young tableau. In particular the occupation numbers of the wavefunction — i.e. the lengths of the columns (rows) of the Young tableau — are fixed through the introduction of Chern-Simons terms. We verify this projection by calculating the number of colour degrees of freedom associated to the matter field. We suggest that, using the worldline approach to quantum field theory, this mechanism will allow the calculation of one-loop scattering amplitudes with the virtual particle in an arbitrary representation of the gauge group.
Morse theory interpretation of topological quantum field theories
International Nuclear Information System (INIS)
Labastida, J.M.F.
1989-01-01
Topological quantum field theories are interpreted as a generalized form of Morse theory. This interpretation is applied to formulate the simplest topological quantum field theory: Topological quantum mechanics. The only non-trivial topological invariant corresponding to this theory is computed and identified with the Euler characteristic. Using field theoretical methods this topological invariant is calculated in different ways and in the process a proof of the Gauss-Bonnet-Chern-Avez formula as well as some results of degenerate Morse theory are obtained. (orig.)
International Nuclear Information System (INIS)
Gerbert, P.S.
1989-01-01
A review of 2+1-dimensional gravity, and recent results concerning the quantum scattering of Klein-Gordon and Dirac test particles in background of point sources with and without spin are presented. The classical theory and general remarks of 2+1 dimensional gravity are reviewed. The space-time in presence of point sources is described. The classical scattering and applications to (Spinning) cosmic strings are discussed. The quantum theory is considered analysing the two body scattering problem. The scattering of spinless particles is discussed including spin-effects. Some classifying remarks about three-dimensional analogue of hte Weyl tensor and Chern-Simons theories of gravitation are also presented. (M.C.K.)