Unification of gauge and gravity Chern-Simons theories in 3-D space-time

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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.)

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)

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

Non abelian Chern-Simons topological coupling from self-interaction

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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 gauge theory on orbifolds: Open strings from three dimensions

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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.

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

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.)

Lorentz-violating Yang-Mills theory. Discussing the Chern-Simons-like term generation

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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.)

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.

All Chern-Simons invariants of 4D, N=1 gauged superform hierarchies

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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 = 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.

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

Anomalous Lorentz and CPT violation from a local Chern-Simons-like term in the effective gauge-field action

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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.

Maxwell-Chern-Simons Casimir effect. II. Circular boundary conditions

International Nuclear Information System (INIS)

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

Mimetic discretization of the Abelian Chern-Simons theory and link invariants

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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.

Chern-Simons gauge theories for the fractional-quantum-Hall-effect hierarchy and anyon superconductivity

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

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.)

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.)

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.)

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

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

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

Asymptotic conformal invariance in a non-Abelian Chern-Simons-matter model

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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

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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].

Self-Dual Configurations in a Generalized Abelian Chern-Simons-Higgs Model with Explicit Breaking of the Lorentz Covariance

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.

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)

Moyal Deformations of Gravity via SU ( N ) Gauge Theories, Branes and Topological Chern-Simons Matrix Models

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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...

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.)

On the phase of Chern-Simons theory with complex gauge group

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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)

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

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.)

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.)

BRST Formalism in Self-Dual Chern-Simons Theory with Matter Fields

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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.

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.))

Chern-Simons terms and cocycles in physics and mathematics

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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)

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.

Entanglement from topology in Chern-Simons theory

Science.gov (United States)

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.

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

Lecture notes on Chern-Simons-Witten theory

CERN Document Server

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

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

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 theory and atypical Hall conductivity in the Varma phase

Science.gov (United States)

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.

A Lie based 4-dimensional higher Chern-Simons theory

Science.gov (United States)

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.

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

Entropy for gravitational Chern-Simons terms by squashed cone method

International Nuclear Information System (INIS)

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.

Once more about the topologically massive gauge theory

International Nuclear Information System (INIS)

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

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)

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.

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

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.

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.

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

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

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

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

Black string first order flow in N=2, d=5 abelian gauged supergravity

Energy Technology Data Exchange (ETDEWEB)

Klemm, Dietmar; Petri, Nicolò; Rabbiosi, Marco [Dipartimento di Fisica, Università di Milano andINFN, Sezione di Milano, Via Celoria 16, I-20133 Milano (Italy)

2017-01-25

We derive both BPS and non-BPS first-order flow equations for magnetically charged black strings in five-dimensional N=2 abelian gauged supergravity, using the Hamilton-Jacobi formalism. This is first done for the coupling to vector multiplets only and U(1) Fayet-Iliopoulos (FI) gauging, and then generalized to the case where also hypermultiplets are present, and abelian symmetries of the quaternionic hyperscalar target space are gauged. We then use these results to derive the attractor equations for near-horizon geometries of extremal black strings, and solve them explicitely for the case where the constants appearing in the Chern-Simons term of the supergravity action satisfy an adjoint identity. This allows to compute in generality the central charge of the two-dimensional conformal field theory that describes the black strings in the infrared, in terms of the magnetic charges, the CY intersection numbers and the FI constants. Finally, we extend the r-map to gauged supergravity and use it to relate our flow equations to those in four dimensions.

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.

''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

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.)

Knot invariants and universal R-matrices from perturbative Chern-Simon theory in the almost axial gauge

International Nuclear Information System (INIS)

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.)

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)

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

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.)

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.

String theory duals of Lifshitz–Chern–Simons gauge theories

International Nuclear Information System (INIS)

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)

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)

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)

Light-front dynamics of Chern-Simons systems

International Nuclear Information System (INIS)

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

On Chern-Simons Matrix Models

CERN Document Server

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.

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

Lattice implementation of Abelian gauge theories with Chern–Simons number and an axion field

Directory of Open Access Journals (Sweden)

Daniel G. Figueroa

2018-01-01

Full Text Available 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(xFμνF˜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→⋅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.

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)

The geometry and physics of Abelian gauge groups in F-theory

Energy Technology Data Exchange (ETDEWEB)

Keitel, Jan

2015-07-14

In this thesis we study the geometry and the low-energy effective physics associated with Abelian gauge groups in F-theory compactifications. To construct suitable torus-fibered Calabi-Yau manifolds, we employ the framework of toric geometry. By identifying appropriate building blocks of Calabi-Yau manifolds that can be studied independently, we devise a method to engineer large numbers of manifolds that give rise to a specified gauge group and achieve a partial classification of toric gauge groups. Extending our analysis from gauge groups to matter spectra, we prove that the matter content of the most commonly studied F-theory set-ups is rather constrained. To circumvent such limitations, we introduce an algorithm to analyze torus-fibrations defined as complete intersections and present several novel kinds of F-theory compactifications. Finally, we show how torus-fibrations without section are linked to fibrations with multiple sections through a network of successive geometric transitions. In order to investigate the low-energy effective physics resulting from our compactifications, we apply M- to F-theory duality. After determining the effective action of F-theory with Abelian gauge groups in six dimensions, we compare the loop-corrected Chern-Simons terms to topological quantities of the compactification manifold to read off the massless matter content. Under certain assumptions, we show that all gravitational and mixed anomalies are automatically canceled in F-theory. Furthermore, we compute the low-energy effective action of F-theory compactifications without section and suggest that the absence of a section signals the presence of an additional massive Abelian gauge field. Adjusting our analysis to four dimensions, we show that remnants of this massive gauge field survive as discrete symmetries that impose selection rules on the Yukawa couplings of the effective theory.

The geometry and physics of Abelian gauge groups in F-theory

International Nuclear Information System (INIS)

Keitel, Jan

2015-01-01

In this thesis we study the geometry and the low-energy effective physics associated with Abelian gauge groups in F-theory compactifications. To construct suitable torus-fibered Calabi-Yau manifolds, we employ the framework of toric geometry. By identifying appropriate building blocks of Calabi-Yau manifolds that can be studied independently, we devise a method to engineer large numbers of manifolds that give rise to a specified gauge group and achieve a partial classification of toric gauge groups. Extending our analysis from gauge groups to matter spectra, we prove that the matter content of the most commonly studied F-theory set-ups is rather constrained. To circumvent such limitations, we introduce an algorithm to analyze torus-fibrations defined as complete intersections and present several novel kinds of F-theory compactifications. Finally, we show how torus-fibrations without section are linked to fibrations with multiple sections through a network of successive geometric transitions. In order to investigate the low-energy effective physics resulting from our compactifications, we apply M- to F-theory duality. After determining the effective action of F-theory with Abelian gauge groups in six dimensions, we compare the loop-corrected Chern-Simons terms to topological quantities of the compactification manifold to read off the massless matter content. Under certain assumptions, we show that all gravitational and mixed anomalies are automatically canceled in F-theory. Furthermore, we compute the low-energy effective action of F-theory compactifications without section and suggest that the absence of a section signals the presence of an additional massive Abelian gauge field. Adjusting our analysis to four dimensions, we show that remnants of this massive gauge field survive as discrete symmetries that impose selection rules on the Yukawa couplings of the effective theory.

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

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 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

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.

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)

Chern-Simons gravity in four dimensions

International Nuclear Information System (INIS)

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.)

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.)

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)

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

Non-minimal Maxwell-Chern-Simons theory and the composite Fermion model

International Nuclear Information System (INIS)

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)

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.

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.

Teichmüller TQFT vs. Chern-Simons theory

Science.gov (United States)

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.

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.)

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.)

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

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.

Introductory lectures on Chern-Simons theories

Science.gov (United States)

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.

Topics in Two-Dimensional Quantum Gravity and Chern-Simons Gauge Theories

Science.gov (United States)

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.).

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.)

Solitons and bubbles in models with Chern-Simons term

International Nuclear Information System (INIS)

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

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

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

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

The Chern-Simons diffusion rate in improved holographic QCD

NARCIS (Netherlands)

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

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

Confinement in Maxwell-Chern-Simons planar quantum electrodynamics and the 1/N approximation

International Nuclear Information System (INIS)

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.

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....

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

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.)

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

The Chern-Simons Current in Systems of DNA-RNA Transcriptions

Science.gov (United States)

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.

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

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.

Anyonic states in Chern-Simons theory

International Nuclear Information System (INIS)

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

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).

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

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.

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

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

Science.gov (United States)

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.

Nontopological bare solutions in the relativistic self-dual Maxwell-Chern-Simons-Higgs model

International Nuclear Information System (INIS)

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

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)

Self-duality in Maxwell-Chern-Simons theories with non minimal coupling with matter field

CERN Document Server

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.

A new gauge for supersymmetric abelian gauge theories

International Nuclear Information System (INIS)

Smith, A.W.; Barcelos Neto, J.

1984-01-01

A new gauge for supersymmetric abelian gauge theories is presented. It is shown that this new gauge allows us to obtain terms which usually come as radiative corrections to the supersymmetric abelian gauge theories when one uses the Wess-Zumino gauge. (Author) [pt

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 ...

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.

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)

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.

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.

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.

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 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.)

Remarks on Chern-Simons Invariants

Science.gov (United States)

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 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.)

Group quantization on configuration space: Gauge symmetries and linear fields

International Nuclear Information System (INIS)

Navarro, M.; Aldaya, V.; Calixto, M.

1997-01-01

A new, configuration-space picture of a formalism of group quantization, the GAQ formalism, is presented in the context of a previous algebraic generalization. This presentation serves to make a comprehensive discussion in which other extensions of the formalism, principally to incorporate gauge symmetries, are developed as well. Both images are combined in order to analyze, in a systematic manner and with complete generality, the case of linear fields (Abelian current groups). To illustrate these developments we particularize them for several fields and, in particular, we carry out the quantization of the Abelian Chern endash Simons models over an arbitrary closed surface in detail. copyright 1997 American Institute of Physics

Superconformal Chern-Simons theories and AdS4/CFT3 correspondence

International Nuclear Information System (INIS)

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.

U(1) x SU(2) Chern-Simons gauge theory of underdoped cuprate superconductors

International Nuclear Information System (INIS)

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

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

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)

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.)

Non-commutative differential calculus and the axial anomaly in Abelian lattice gauge theories

International Nuclear Information System (INIS)

Fujiwara, Takanori; Suzuki, Hiroshi; Wu, Ke

2000-01-01

The axial anomaly in lattice gauge theories has a topological nature when the Dirac operator satisfies the Ginsparg-Wilson relation. We study the axial anomaly in Abelian gauge theories on an infinite hypercubic lattice by utilizing cohomological arguments. The crucial tool in our approach is the non-commutative differential calculus (NCDC) which makes the Leibniz rule of exterior derivatives valid on the lattice. The topological nature of the 'Chern character' on the lattice becomes manifest in the context of NCDC. Our result provides an algebraic proof of Luescher's theorem for a four-dimensional lattice and its generalization to arbitrary dimensions

Banados-Teitelboim-Zanelli black hole with gravitational Chern-Simons term: Thermodynamics and statistical entropy

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

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

Non-Abelian gauge fields

Science.gov (United States)

Gerbier, Fabrice; Goldman, Nathan; Lewenstein, Maciej; Sengstock, Klaus

2013-07-01

coupling) and also introduces novel kinds of exotic Hamiltonians. Goldman et al [10] propose a concrete setup for realizing arbitrary non-Abelian gauge potentials in optical square lattices; they discuss how such synthetic gauge fields can be exploited to generate Chern insulators. Zygelman [11], similarly as Kiffner et al [8], discusses in his paper non-Abelian gauge fields in Rydberg systems. Marchukov et al [12] return to the subject of spin-orbit coupling, and investigate spectral gaps of spin-orbit coupled particles in the realistic situations of deformed traps. The last two papers, in contrast, are devoted to different subjects. Edmonds et al [13] consider a 'dynamical' density-dependent gauge potential, and study the Josephson effect in a Bose-Einstein condensate subject to such a potential. Last, but not least, Mazzucchi et al [14] study the properties of semimetal-superfluid quantum phase transitions in 3D lattices with Dirac points. References [1] Zhou X, Li Y, Cai Z and Wu C 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134001 [2] Maldonado-Mundo D, Öhberg P and Valiente M 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134002 [3] Anderson B M and Clark C W 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134003 [4] Orth P P, Cocks D, Rachel S, Buchhold M, Le Hur K and Hofstetter W 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134004 [5] Nascimbène S 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134005 [6] Graß T, Juliá-Díaz B, Burrello M and Lewenstein M 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134006 [7] Zheng W, Yu Z-Q, Cui X and Zhai H 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134007 [8] Kiffner M, Li W and Jaksch D 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134008 [9] Shenoy V B and Vyasanakere J P 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134009 [10] Goldman N, Gerbier F and Lewenstein M 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134010 [11] Zygelman B 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134011 [12] Marchukov O V, Volosniev A G, Fedorov D V, Jensen A S and Zinner N T 2013 J. Phys. B: At. Mol

Abelian 2-form gauge theory: special features

International Nuclear Information System (INIS)

Malik, R P

2003-01-01

It is shown that the four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory provides an example of (i) a class of field theoretical models for the Hodge theory, and (ii) a possible candidate for the quasi-topological field theory (q-TFT). Despite many striking similarities with some of the key topological features of the two (1 + 1)-dimensional (2D) free Abelian (and self-interacting non-Abelian) gauge theories, it turns out that the 4D free Abelian 2-form gauge theory is not an exact TFT. To corroborate this conclusion, some of the key issues are discussed. In particular, it is shown that the (anti-)BRST and (anti-)co-BRST invariant quantities of the 4D 2-form Abelian gauge theory obey recursion relations that are reminiscent of the exact TFTs but the Lagrangian density of this theory is not found to be able to be expressed as the sum of (anti-)BRST and (anti-)co-BRST exact quantities as is the case with the topological 2D free Abelian (and self-interacting non-Abelian) gauge theories

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.

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

Large data well-posedness in the energy space of the Chern-Simons-Schrödinger system

Science.gov (United States)

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.

Towards a realization of the condensed-matter-gravity correspondence in string theory via consistent Abelian truncation of the Aharony-Bergman-Jafferis-Maldacena model.

Science.gov (United States)

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.

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.

2+1 topological term, anyons and their possible application in high Tc superconductivity

International Nuclear Information System (INIS)

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

SU(2) gauge theory in the maximally Abelian gauge without monopoles

International Nuclear Information System (INIS)

Shmakov, S.Yu.; Zadorozhnyj, A.M.

1995-01-01

We present an algorithm for simulation of SU(2) lattice gauge theory under the maximally Abelian (MA) gauge and first numerical results for the theory without Abelian monopoles. The results support the idea that nonperturbative interaction arises between monopoles and residual Abelian field and the other interactions are perturbative. It is shown that the Gribov region for the theory with the MA gauge fixed is non-connected. 12 refs., 1 tab

Pure Lovelock gravity and Chern-Simons theory

Science.gov (United States)

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.

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.

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).

Scattering amplitude and bosonization duality in general Chern-Simons vector models

Science.gov (United States)

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.

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.

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

What we think about the higher dimensional Chern-Simons theories

International Nuclear Information System (INIS)

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

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

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.)

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

Chern-Simons expectation values and quantum horizons from loop quantum gravity and the Duflo map.

Science.gov (United States)

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.

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...

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.

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

Non-Abelian gauge fields in two spatial dimensions

International Nuclear Information System (INIS)

Hagen, C.R.

1987-01-01

Generalizing an earlier work on the Abelian case the most general non-Abelian gauge theory in two spatial dimensions is derived. It is shown that local gauge invariance leads to a new term in the action which in turn requires that the gauge current operator have a part which is bilinear in the non-Abelian gauge field-strength tensor. Although a radiation (or axial) gauge quantization is possible, this approach is found not to yield the maximal set of commutation relations among the basic fields. The latter goal can be accomplished only by a rather unusual gauge choice which has not previously been studied. Quantization conditions on the coupling constant implied by invariance under large gauge transformations are also derived

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

Integrable spin chain in superconformal Chern-Simons theory

International Nuclear Information System (INIS)

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.

Renormalizable Abelian-projected effective gauge theory derived from quantum chromodynamics

International Nuclear Information System (INIS)

Kondo, Kei-ichi; Shinohara, Toru

2001-01-01

We show that an effective Abelian gauge theory can be obtained as a renormalizable theory from QCD in the maximal Abelian gauge. The derivation improves in a systematic manner the previous version that was obtained by one of the authors and was referred to as the Abelian-projected effective gauge theory. This result supports the view that we can construct an effective Abelian gauge theory from QCD without losing characteristic features of the original non-Abelian gauge theory. In fact, it is shown that the effective coupling constant in the resulting renormalizable theory has a renormalization-scale dependence governed by the β-function that is exactly the same as that of the original Yang-Mills theory, irrespective of the choice of gauge fixing parameters of the maximal Abelian gauge and the parameters used for identifying the dual variables. Moreover, we evaluate the anomalous dimensions of the fields and parameters in the resultant theory. By choosing the renormalized parameters appropriately, we can switch the theory into an electric or a magnetic theory. (author)

Gauge-invariant factorization and canonical quantization of topologically massive gauge theories in any dimension

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

Signature of biased range in the non-dynamical Chern-Simons modified gravity and its measurements with satellite-satellite tracking missions: theoretical studies

Science.gov (United States)

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.

Non-Abelian Gauge Theory in the Lorentz Violating Background

Science.gov (United States)

Ganai, Prince A.; Shah, Mushtaq B.; Syed, Masood; Ahmad, Owais

2018-03-01

In this paper, we will discuss a simple non-Abelian gauge theory in the broken Lorentz spacetime background. We will study the partial breaking of Lorentz symmetry down to its sub-group. We will use the formalism of very special relativity for analysing this non-Abelian gauge theory. Moreover, we will discuss the quantisation of this theory using the BRST symmetry. Also, we will analyse this theory in the maximal Abelian gauge.

Topological charge in non-abelian lattice gauge theory

International Nuclear Information System (INIS)

Lisboa, P.

1983-01-01

We report on a numerical calculation of topological charge densities in non-abelian gauge theory with gauge groups SU(2) and SU(3). The group manifold is represented by a discrete subset thereof which lies outside its finite subgroups. The results shed light on the usefulness of these representations in Monte Carlo evaluations of non-abelian lattice gauge theory. (orig.)

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

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.

Chern-Simons (super)gravity

CERN Document Server

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...

Does the Higgs mechanism favour electron-electron bound states in Maxwell-Chern-Simons QED3?

International Nuclear Information System (INIS)

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)

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)

Some aspects of non-Abelian gauge theories

International Nuclear Information System (INIS)

Tyburski, L.J.

1976-01-01

Two aspects of the theory of non-Abelian gauge fields are considered. In the first part, the fermion-fermion scattering amplitude is calculated for a non-Abelian gauge theory with SU(N) gauge symmetry in the limit of high energy with fixed momentum transfer through sixth order in the coupling constant. Only the leading logarithmic terms in each order of perturbation theory are kept. To avoid the infrared problem, the Higgs mechanism is invoked to give masses to the vector bosons of the theory. It is found that the scattering amplitude exponentiates to a Regge form. This result is qualitatively different from an earlier published calculation. In the second part of the thesis, we consider fermion-fermion scattering in a non-Abelian gauge theory with massless vector bosons, and demonstrate that for physically measurable cross sections the infrared divergences of the theory cancel out to lowest nontrivial order

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

Non-abelian bosonization in two-dimensional condensed matter physics

International Nuclear Information System (INIS)

Froehlich, J.; Kerler, T.; Marchetti, P.A.

1992-01-01

We derive mathematical identities proving that some systems of interacting, non-relativistic fermions of spin or 'isospin' S=1/2, 3/3, 5/2, ... confined to a plane (e.g. a heterojuncture) can be described in terms of a complex boson of spin or isospin S coupled to statistical U(1) and SU(2) gauge fields. In a Feynman path integral formulation, the U(1) gauge field has a Chern-Simons action with coupling constant k=2/(2l+1), l=0, 1, 2, ..., while the SU(2) gauge field has a Chern-Simons action with level 2S. Generalization to internal symmetry groups other than SU(2) are sketched, and applications of our formalism to an analysis of excitations with braid statistics in incompressible quantum fluids and of holons and spinons in the t-J model are discussed. (orig.)

Quantum field theory I foundations and Abelian and non-Abelian gauge theories

CERN Document Server

Manoukian, Edouard B

2016-01-01

This textbook covers a broad spectrum of developments in QFT, emphasizing those aspects that are now well consolidated and for which satisfactory theoretical descriptions have been provided. The book is unique in that it offers a new approach to the subject and explores many topics merely touched upon, if covered at all, in standard reference works. A detailed and largely non-technical introductory chapter traces the development of QFT from its inception in 1926. The elegant functional differential approach put forward by Schwinger, referred to as the quantum dynamical (action) principle, and its underlying theory are used systematically in order to generate the so-called vacuum-to-vacuum transition amplitude of both abelian and non-abelian gauge theories, in addition to Feynman’s well-known functional integral approach, referred to as the path-integral approach. Given the wealth of information also to be found in the abelian case, equal importance is put on both abelian and non-abelian gauge theories. Pa...

Papapetrou energy-momentum tensor for Chern-Simons modified gravity

International Nuclear Information System (INIS)

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

Superspace formulation in a three-algebra approach to D=3, N=4, 5 superconformal Chern-Simons matter theories

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.

Dual potentials in non-Abelian gauge theories

International Nuclear Information System (INIS)

Caticha, A.

1988-01-01

Motivated by the possibility that confinement and superconductivity are similar phenomena, dual potentials are introduced into Yang-Mills theory in two different ways. Both are extensions of Zwanziger's two-potential formalism for Abelian charges and monopoles to the non-Abelian case. In the first approach the dual potentials carry a color index and there is a rather simple, although nonlocal, dual-variable formulation. In the second approach dual variables are introduced into the so-called Abelian projection of the SU(2) Yang-Mills theory. An interesting feature is that the quartic contact interactions are absent and there is a special gauge choice for which the theory takes on a ''purely electromagnetic'' form. More important, however, is the appearance of an additional Abelian magnetic gauge symmetry the dynamical breaking of which may be associated with confinement

Fractional exclusion and braid statistics in one dimension: a study via dimensional reduction of Chern-Simons theory

Science.gov (United States)

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.

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.

Localization of abelian gauge fields on thick branes

Energy Technology Data Exchange (ETDEWEB)

Vaquera-Araujo, Carlos A. [Universidad de Colima, Facultad de Ciencias, CUICBAS, Colima (Mexico); Corradini, Olindo [Universidad Autonoma de Chiapas, Ciudad Universitaria, Facultad de Ciencias en Fisica y Matematicas, Tuxtla Gutierrez (Mexico); Universita di Modena e Reggio Emilia, Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Modena (Italy)

2015-02-01

In this work, we explore a mechanism for abelian gauge field localization on thick branes based on a five-dimensional Stueckelberg-like action. A normalizable zero mode is found through the identification of a suitable coupling function between the brane and the gauge field. The same mechanism is studied for the localization of the abelian Kalb-Ramond field. (orig.)

Gauge-preheating and the end of axion inflation

Energy Technology Data Exchange (ETDEWEB)

Adshead, Peter; Sfakianakis, Evangelos I. [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801 (United States); Giblin, John T. Jr.; Scully, Timothy R., E-mail: adshead@illinois.edu, E-mail: giblinj@kenyon.edu, E-mail: tscully2@illinois.edu, E-mail: esfaki@illinois.edu [Department of Physics, Kenyon College, 201 North College Rd, Gambier, Ohio 43022 (United States)

2015-12-01

We study the onset of the reheating epoch at the end of axion-driven inflation where the axion is coupled to an Abelian, U(1), gauge field via a Chern-Simons interaction term. We focus primarily on m{sup 2φ2} inflation and explore the possibility that preheating can occur for a range of coupling values consistent with recent observations and bounds on the overproduction of primordial black holes. We find that for a wide range of parameters preheating is efficient. In certain cases the inflaton transfers all of its energy to the gauge fields within a few oscillations. In most cases, we find that the gauge fields on sub-horizon scales end preheating in an unpolarized state due to the existence of strong rescattering between the inflaton and gauge-field modes. We also present a preliminary study of an axion monodromy model coupled to U(1) gauge fields, seeing a similarly efficient preheating behavior as well as indications that the coupling strength has an effect on the creation of oscillons.

Gauge-preheating and the end of axion inflation

International Nuclear Information System (INIS)

Adshead, Peter; Sfakianakis, Evangelos I.; Giblin, John T. Jr.; Scully, Timothy R.

2015-01-01

We study the onset of the reheating epoch at the end of axion-driven inflation where the axion is coupled to an Abelian, U(1), gauge field via a Chern-Simons interaction term. We focus primarily on m 2φ2 inflation and explore the possibility that preheating can occur for a range of coupling values consistent with recent observations and bounds on the overproduction of primordial black holes. We find that for a wide range of parameters preheating is efficient. In certain cases the inflaton transfers all of its energy to the gauge fields within a few oscillations. In most cases, we find that the gauge fields on sub-horizon scales end preheating in an unpolarized state due to the existence of strong rescattering between the inflaton and gauge-field modes. We also present a preliminary study of an axion monodromy model coupled to U(1) gauge fields, seeing a similarly efficient preheating behavior as well as indications that the coupling strength has an effect on the creation of oscillons

Higgs phase in non-Abelian gauge theories

International Nuclear Information System (INIS)

Kaymakcalan, O.S.

1981-06-01

A non-Abelian gauge theory involving scalar fields with non-tachyonic mass terms in the Lagrangian is considered, in order to construct a finite energy density trial vacuum for this theory. The usual scalar potential arguments suggest that the vacuum of such a theory would be in the perturbative phase. However, the obvious choices for a vacuum in this phase, the Axial gauge and the Coulomb gauge bare vacua, do not have finite energy densities even with an ultraviolet cutoff. Indeed, it is a non-trivial problem to construct finite energy density vacua for non-Abelian gauge theories and this is intimately connected with the gauge fixing degeneracies of these theories. Since the gauge fixing is achieved in the Unitary gauge, this suggests that the Unitary gauge bare vacuum might be a finite energy trial vacuum and, despite the form of the scalar potential, the vacuum of this theory might be in a Higgs phase rather than the perturbative phase

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

Science.gov (United States)

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.)

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.))

Multi-cut solutions in Chern-Simons matrix models

Science.gov (United States)

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.

Classical optics in generalized Maxwell Chern-Simons theory

International Nuclear Information System (INIS)

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

Wilson loops in superconformal Chern-Simons theory and fundamental strings in Anti-de Sitter supergravity dual

International Nuclear Information System (INIS)

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.

Non Abelian T-duality in Gauged Linear Sigma Models

Science.gov (United States)

Bizet, Nana Cabo; Martínez-Merino, Aldo; Zayas, Leopoldo A. Pando; Santos-Silva, Roberto

2018-04-01

Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM's as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they depend in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.

Unveiling a spinor field classification with non-Abelian gauge symmetries

Science.gov (United States)

Fabbri, Luca; da Rocha, Roldão

2018-05-01

A spinor fields classification with non-Abelian gauge symmetries is introduced, generalizing the U(1) gauge symmetries-based Lounesto's classification. Here, a more general classification, contrary to the Lounesto's one, encompasses spinor multiplets, corresponding to non-Abelian gauge fields. The particular case of SU(2) gauge symmetry, encompassing electroweak and electromagnetic conserved charges, is then implemented by a non-Abelian spinor classification, now involving 14 mixed classes of spinor doublets. A richer flagpole, dipole, and flag-dipole structure naturally descends from this general classification. The Lounesto's classification of spinors is shown to arise as a Pauli's singlet, into this more general classification.

Abelian gauge symmetries in F-theory and dual theories

Science.gov (United States)

Song, Peng

In this dissertation, we focus on important physical and mathematical aspects, especially abelian gauge symmetries, of F-theory compactifications and its dual formulations within type IIB and heterotic string theory. F-theory is a non-perturbative formulation of type IIB string theory which enjoys important dualities with other string theories such as M-theory and E8 x E8 heterotic string theory. One of the main strengths of F-theory is its geometrization of many physical problems in the dual string theories. In particular, its study requires a lot of mathematical tools such as advanced techniques in algebraic geometry. Thus, it has also received a lot of interests among mathematicians, and is a vivid area of research within both the physics and the mathematics community. Although F-theory has been a long-standing theory, abelian gauge symmetry in Ftheory has been rarely studied, until recently. Within the mathematics community, in 2009, Grassi and Perduca first discovered the possibility of constructing elliptically fibered varieties with non-trivial toric Mordell-Weil group. In the physics community, in 2012, Morrison and Park first made a major advancement by constructing general F-theory compactifications with U(1) abelian gauge symmetry. They found that in such cases, the elliptically-fibered Calabi-Yau manifold that F-theory needs to be compactified on has its fiber being a generic elliptic curve in the blow-up of the weighted projective space P(1;1;2) at one point. Subsequent developments have been made by Cvetic, Klevers and Piragua extended the works of Morrison and Park and constructed general F-theory compactifications with U(1) x U(1) abelian gauge symmetry. They found that in the U(1) x U(1) abelian gauge symmetry case, the elliptically-fibered Calabi-Yau manifold that F-theory needs to be compactified on has its fiber being a generic elliptic curve in the del Pezzo surface dP2. In chapter 2 of this dissertation, I bring this a step further by

Maximal Abelian gauge and a generalized BRST transformation

Directory of Open Access Journals (Sweden)

Shinichi Deguchi

2016-05-01

Full Text Available We apply a generalized Becchi–Rouet–Stora–Tyutin (BRST formulation to establish a connection between the gauge-fixed SU(2 Yang–Mills (YM theories formulated in the Lorenz gauge and in the Maximal Abelian (MA gauge. It is shown that the generating functional corresponding to the Faddeev–Popov (FP effective action in the MA gauge can be obtained from that in the Lorenz gauge by carrying out an appropriate finite and field-dependent BRST (FFBRST transformation. In this procedure, the FP effective action in the MA gauge is found from that in the Lorenz gauge by incorporating the contribution of non-trivial Jacobian due to the FFBRST transformation of the path integral measure. The present FFBRST formulation might be useful to see how Abelian dominance in the MA gauge is realized in the Lorenz gauge.

Effective monopole potential for SU(2) lattice gluodynamics in spatial maximal Abelian gauge

International Nuclear Information System (INIS)

Chernodub, M.N.; Polikarpov, M.I.; Veselov, A.I.

1999-01-01

We investigate the dual superconductor hypothesis in finite-temperature SU(2) lattice gluodynamics in the Spatial Maximal Abelian gauge. This gauge is more physical than the ordinary Maximal Abelian gauge due to absence of non-localities in temporal direction. We shown numerically that in the Spatial Maximal Abelian gauge the probability distribution of the abelian monopole field is consistent with the dual superconductor mechanism of confinement [ru

N=1,2 supergravities in 2+1 dimensions as Chern-Simons theories

International Nuclear Information System (INIS)

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

Medium generated gap in gravity and a 3D gauge theory

Science.gov (United States)

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.

Abelian color cycles: A new approach to strong coupling expansion and dual representations for non-abelian lattice gauge theory

Energy Technology Data Exchange (ETDEWEB)

Gattringer, Christof, E-mail: christof.gattringer@uni-graz.at; Marchis, Carlotta, E-mail: carla.marchis@uni-graz.at

2017-03-15

We propose a new approach to strong coupling series and dual representations for non-abelian lattice gauge theories using the SU(2) case as an example. The Wilson gauge action is written as a sum over “abelian color cycles” (ACC) which correspond to loops in color space around plaquettes. The ACCs are complex numbers which can be commuted freely such that the strong coupling series and the dual representation can be obtained as in the abelian case. Using a suitable representation of the SU(2) gauge variables we integrate out all original gauge links and identify the constraints for the dual variables in the SU(2) case. We show that the construction can be generalized to the case of SU(2) gauge fields with staggered fermions. The result is a strong coupling series where all gauge integrals are known in closed form and we discuss its applicability for possible dual simulations. The abelian color cycle concept can be generalized to other non-abelian gauge groups such as SU(3).

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

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.

Boundary effects in 2 + 1 dimensional Maxwell-Chern-Simons theory

International Nuclear Information System (INIS)

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

Possible physical manifestation of the Weyl non-Abelian gauge field

International Nuclear Information System (INIS)

Barbashov, B.M.; Pestov, A.B.

1998-01-01

On the basis of the Weyl equations of congruent transference, we consider a possible influence of the Weyl non-Abelian gauge field defining the transference on the precession of a gyroscope. Plane-wave solutions to the equations of the Abelian gauge field are derived

Chern-Simons, Wess-Zumino and other cocycles from Kashiwara-Vergne and associators

Science.gov (United States)

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.

Flat connections in three-manifolds and classical Chern–Simons 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 Chern–Simons 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 π1(M and by the Heegaard gluing homeomorphism. Examples of flat connections in topologically nontrivial manifolds are presented and the computations of the associated classical Chern–Simons invariants are illustrated.

Anomalous Lorentz and CPT violation from a local Chern–Simons-like term in the effective gauge-field action

Directory of Open Access Journals (Sweden)

K.J.B. Ghosh

2018-01-01

Full Text Available 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.

ADHM and the 4d quantum Hall effect

Science.gov (United States)

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.

Instantons and Gribov copies in the maximally Abelian gauge

International Nuclear Information System (INIS)

Bruckmann, F.; Heinzl, T.; Wipf, A.; Tok, T.

2000-01-01

We calculate the Faddeev-Popov operator corresponding to the maximally Abelian gauge for gauge group SU(N). Specializing to SU(2) we look for explicit zero modes of this operator. Within an illuminating toy model (Yang-Mills mechanics) the problem can be completely solved and understood. In the field theory case we are able to find an analytic expression for a normalizable zero mode in the background of a single 't Hooft instanton. Accordingly, such an instanton corresponds to a horizon configuration in the maximally Abelian gauge. Possible physical implications are discussed

Differential geometry construction of anomalies and topological invariants in various dimensions

CERN Document Server

Antoniadis, Ignatios

2012-01-01

The Lagrangian of non-Abelian tensor gauge fields describes interaction of the Yang-Mills field and massless tensor gauge bosons of increasing helicities. The model allows the existence of metric-independent densities: the exact (2n+3)-forms and their secondary characteristics, the (2n+2)-forms. We also found exact 6n-forms and the corresponding secondary (6n-1)-forms. These forms are the analogs of the Pontryagin densities: the exact 2n-forms and Chern-Simons secondary characteristics, the (2n-1)-forms. The (2n+3)- and 6n-forms are gauge invariant densities, while the (2n+2)- and (6n-1)-forms transform non-trivially under gauge transformations, that we compare with the corresponding transformations of the Chern-Simons secondary characteristics. This construction allows to identify new potential anomalies in various dimensions.

Dirac matrices for Chern-Simons gravity

Energy Technology Data Exchange (ETDEWEB)

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.

Charges and Energy in Chern-Simons Theories and Lovelock Gravity

OpenAIRE

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...

High-energy behavior of non-Abelian gauge theories

International Nuclear Information System (INIS)

Nieh, H.T.; Yao, Y.

1976-01-01

This paper is a detailed account of a study in perturbation theory of the high-energy behavior of non-Abelian gauge theories. The fermion-fermion scattering amplitude is calculated up to sixth order in the coupling constant in the high-energy limit s → infinity with fixed t, in the approximation of keeping only the leading logarithmic terms. Results indicate that the high-energy behavior of non-Abelian gauge theories are complicated, and quite different from the known behaviors of other field theories studied so far

Spontaneously broken abelian gauge invariant supersymmetric model

International Nuclear Information System (INIS)

Mainland, G.B.; Tanaka, K.

A model is presented that is invariant under an Abelian gauge transformation and a modified supersymmetry transformation. This model is broken spontaneously, and the interplay between symmetry breaking, Goldstone particles, and mass breaking is studied. In the present model, spontaneously breaking the Abelian symmetry of the vacuum restores the invariance of the vacuum under a modified supersymmetry transformation. (U.S.)

Central extensions of some Abelian finite gauge groups

International Nuclear Information System (INIS)

Combe, Ph.; Rodriguez, R.; Sirugue, M.; Sirugue-Collin, M.

1981-01-01

The authors describe central extensions of Abelian finite gauge groups on lattices which are permutation invariant. Moreover some remarks are made on the gauge models on lattice associated with these non-commutative central extensions. (Auth.)

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)

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

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 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)

Free Abelian 2-form gauge theory: BRST approach

International Nuclear Information System (INIS)

Malik, R.P.

2008-01-01

We discuss various symmetry properties of the Lagrangian density of a four- (3+1)-dimensional (4D) free Abelian 2-form gauge theory within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. The present free Abelian gauge theory is endowed with a Curci-Ferrari type condition, which happens to be a key signature of the 4D non-Abelian 1-form gauge theory. In fact, it is due to the above condition that the nilpotent BRST and anti-BRST symmetries of our present theory are found to be absolutely anticommuting in nature. For the present 2-form theory, we discuss the BRST, anti-BRST, ghost and discrete symmetry properties of the Lagrangian densities and derive the corresponding conserved charges. The algebraic structure, obeyed by the above conserved charges, is deduced and the constraint analysis is performed with the help of physicality criteria, where the conserved and nilpotent (anti-)BRST charges play completely independent roles. These physicality conditions lead to the derivation of the above Curci-Ferrari type restriction, within the framework of the BRST formalism, from the constraint analysis. (orig.)

Non-Abelian duality in N = 4 supersymmetric gauge theories

International Nuclear Information System (INIS)

Dorey, Nicholas; Fraser, Christophe; Hollowood, Timithy J.; Kneipp, Marco A.C.

1996-03-01

A semi-classical check of the Goddard-Nuyts-Olive (GNO) generalized duality conjecture for gauge theories with adjoint Higgs fields is performed for the case where the unbroken gauge group is non-Abelian. The monopole solutions of the theory transform under the non-Abelian part of the unbroken global symmetry and the associated component of the moduli space is a Lie group coset space. The well-known problems in introducing collective coordinates for these degrees-of-freedom are solved by considering suitable multi monopole configurations in which the long-range non-Abelian fields cancel. In the context of an N = 4 supersymmetric gauge theory, the multiplicity of BPS saturated states is given by the number of ground-states of a supersymmetric quantum mechanics on the compact internal moduli space. The resulting degeneracy is expressed as the Euler character of the coset space. In all cases the number of states is consistent with the dimensions of the multiplets of the unbroken dual gauge group, and hence the results provide strong support for the GNO conjecture. (author). 39 refs

Problem of colour confinement in non-Abelian gauge theories

International Nuclear Information System (INIS)

Gribov, V.N.

1978-01-01

The problem of the colour confinement in the non-abelian gauge theories is studied. A more rigorous treatment of the Fadeev-Popov procedure for the quantization of the non-abelian gauge theories is presented. In the improved procedure one has to introduce additional bounds on the region of integration in the functional space of non-abelian fields. The integration is to be performed over the fields with positive-definite Faddeev-Popov determinant. This limitation has little influence on oscillations with high frequencies, but reduces drastically the amplitudes of low-frequency oscillations. This implies, that interaction of two colour charges does not go into infinity at finite distances, rather it is linearly rising with distance

On the loop-loop scattering amplitudes in Abelian and non-Abelian gauge theories

International Nuclear Information System (INIS)

Meggiolaro, Enrico

2005-01-01

The high-energy elastic scattering amplitude of two colour-singlet qq-bar pairs is governed by the correlation function of two Wilson loops, which follow the classical straight lines for quark (antiquark) trajectories. This quantity is expected to be free of IR divergences, differently from what happens for the parton-parton elastic scattering amplitude, described, in the high-energy limit, by the expectation value of two Wilson lines. We shall explicitly test this IR finiteness by a direct non-perturbative computation of the loop-loop scattering amplitudes in the (pedagogic, but surely physically interesting) case of quenched QED. The results obtained for the Abelian case will be generalized to the case of a non-Abelian gauge theory with Nc colours, but stopping to the order O(g4) in perturbation theory. In connection with the above-mentioned IR finiteness, we shall also discuss some analytic properties of the loop-loop scattering amplitudes in both Abelian and non-Abelian gauge theories, when going from Minkowskian to Euclidean theory, which can be relevant to the still unsolved problem of the s-dependence of hadron-hadron total cross-sections

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.

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

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.)

Metal-Insulator Transition Revisited for Cold Atoms in Non-Abelian Gauge Potentials

International Nuclear Information System (INIS)

Satija, Indubala I.; Dakin, Daniel C.; Clark, Charles W.

2006-01-01

We discuss the possibility of realizing metal-insulator transitions with ultracold atoms in two-dimensional optical lattices in the presence of artificial gauge potentials. For Abelian gauges, such transitions occur when the magnetic flux penetrating the lattice plaquette is an irrational multiple of the magnetic flux quantum. Here we present the first study of these transitions for non-Abelian U(2) gauge fields. In contrast to the Abelian case, the spectrum and localization transition in the non-Abelian case is strongly influenced by atomic momenta. In addition to determining the localization boundary, the momentum fragments the spectrum. Other key characteristics of the non-Abelian case include the absence of localization for certain states and satellite fringes around the Bragg peaks in the momentum distribution and an interesting possibility that the transition can be tuned by the atomic momenta

Non-Abelian formulation of a vector-tensor gauge theory with topological coupling

International Nuclear Information System (INIS)

Barcelos Neto, J.; Cabo, A.; Silva, M.B.D.

1995-08-01

We obtain a non-Abelian version of a theory involving vector and tensor and tensor gauge fields interacting via a massive topological coupling, besides the nonminimum one. The new fact is that the non-Abelian theory is not reducible and Stuckelberg fields are introduced in order to compatibilize gauge invariance, nontrivial physical degrees of freedom and the limit of the Abelian case. (author). 9 refs

From Lorentz-Chern-Simons to Massive Gravity in 2+1 dimensions

Energy Technology Data Exchange (ETDEWEB)

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.

Local observables in non-Abelian gauge theories

International Nuclear Information System (INIS)

Sharatchandra, H.S.

1981-09-01

Labelling of the physical states of a non-Abelian gauge theory on a lattice in terms of local observables in considered. The labelling is in terms of local color electric field observables and (separately) local color magnetic field observables. Matter field is also included. The non-local variables required when space is multiply-connected, are specified. Non-Abelian version of the Stokes' theorem is considered. Relevance to the continuum theory is discussed in detail. (orig.)

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.

Problems of an external field in non-Abelian gauge theory

International Nuclear Information System (INIS)

Gavrilov, S.P.; Gitman, D.M.

1992-01-01

In the Abelian gauge field theory QED the principal problems connected with an external field are the problems of exact keeping of an external field in a perturbation theory and appearing in this case the peculiarities of the theory such as the instability of the vacuum and so on. There is the problem of an external field introduction or its interpretation side by side with this problem in Non-Abelian gauge theory. The solution of both these problems in Non-Abelian theory can be considered by analogy with QED. In the present paper, the authors discuss on the example of the spontaneously broken SU(2) x U(1) electroweak theory both the problems of an external field introduction and the problem of exact keeping of this field in the perturbation theory. The Langrangian of this theory in covariant gauge is chosen in the BRST invariant form. In spite of concrete character of the theory studied, the method can be extended to any gauge theory

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.

Non-Abelian gauge theory of fields associated with dyons

International Nuclear Information System (INIS)

Rajput, B.S.; Kumar, S.R.

1983-01-01

A suitable Lorentz invariant non-Abelian gauge theory of the fields associated with dyons has been constructed to describe the dual dynamics between colour isocharges and topological charges. It has been shown that the generalized particle current is gauge covariant and not conserved in non-Abelian theory. It has also been shown that in this theory the unphysical string variables and unphysical charged fields are not needed and that any extra constraint to maintain the dual symmetry of field equation and Lagrangian is also not needed. (author)

Hydrodynamic electron flow in a Weyl semimetal slab: Role of Chern-Simons terms

Science.gov (United States)

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.

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

Gravitational waves from non-Abelian gauge fields at a tachyonic transition

Science.gov (United States)

Tranberg, Anders; Tähtinen, Sara; Weir, David J.

2018-04-01

We compute the gravitational wave spectrum from a tachyonic preheating transition of a Standard Model-like SU(2)-Higgs system. Tachyonic preheating involves exponentially growing IR modes, at scales as large as the horizon. Such a transition at the electroweak scale could be detectable by LISA, if these non-perturbatively large modes translate into non-linear dynamics sourcing gravitational waves. Through large-scale numerical simulations, we find that the spectrum of gravitational waves does not exhibit such IR features. Instead, we find two peaks corresponding to the Higgs and gauge field mass, respectively. We find that the gravitational wave production is reduced when adding non-Abelian gauge fields to a scalar-only theory, but increases when adding Abelian gauge fields. In particular, gauge fields suppress the gravitational wave spectrum in the IR. A tachyonic transition in the early Universe will therefore not be detectable by LISA, even if it involves non-Abelian gauge fields.

Fermion-dyon dynamics in non-Abelian gauge theory

International Nuclear Information System (INIS)

Pant, P.C.; Pandey, V.P.; Rajput, B.S.

1999-01-01

The study of behaviour of a fermion in the field of non-Abelian dyon has been undertaken in Lagrangian and Hamiltonian formulation. Solving Dirac equation, expression for energy Eigen value has been obtained and the Hamiltonian of this system has been shown to involve spin as well as contribution of massive fields associated with these particles. By introducing suitable spinors, the Pauli equation for a dyon moving in the field of fermion has been solved in non-Abelian gauge gauge theory and it is shown that introduction of massive fields perceptibly modifies the energy Eigen value and Eigen function of bound states of the system. (author)

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

Topological resolution of gauge theory singularities

Science.gov (United States)

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.

Anomaly cancellation condition in abelian lattice gauge theories

International Nuclear Information System (INIS)

Suzuki, Hiroshi

1999-11-01

We analyze the general solution of the Wess-Zumino consistency condition in abelian lattice gauge theories, without taking the classical continuum limit. We find that, if the anomaly density is a local pseudo-scalar field on the lattice, the non-trivial anomaly is always proportional to the anomaly coefficient in the continuum theory. The possible extension of this result to non-abelian theories is briefly discussed. (author)

Super-Chern-Simons Theory as Superstring Theory

CERN Document Server

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.

Construction of non-Abelian gauge theories on noncommutative spaces

International Nuclear Information System (INIS)

Jurco, B.; Schupp, P.; Moeller, L.; Wess, J.; Max-Planck-Inst. fuer Physik, Muenchen; Humboldt-Univ., Berlin; Schraml, S.; Humboldt-Univ., Berlin

2001-01-01

We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories. (orig.)

Construction of non-Abelian gauge theories on noncommutative spaces

Energy Technology Data Exchange (ETDEWEB)

Jurco, B.; Schupp, P. [Sektion Physik, Muenchen Univ. (Germany); Moeller, L.; Wess, J. [Sektion Physik, Muenchen Univ. (Germany); Max-Planck-Inst. fuer Physik, Muenchen (Germany); Humboldt-Univ., Berlin (Germany). Inst. fuer Physik; Schraml, S. [Sektion Physik, Muenchen Univ. (Germany)

2001-06-01

We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories. (orig.)

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)

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

Non-abelian gauge invariant classical Lagrangian formalism for point electric and magnetic charge

International Nuclear Information System (INIS)

Brandt, R.A.; Neri, F.

1978-01-01

The classical electrodynamics of electrically charged point particles has been generalized to include non-Abelian gauge groups and to include magnetically charged point particles. In this paper these two distinct generalizations are unified into a non-Abelian gauge theory of electric and magnetic charge. Just as the electrically charged particles constitute the generalized source of the gauge fields, the magnetically charged particles constitute the generalized source of the dual fields. The resultant equations of motion are invariant to the original 'electric' non-Abelian gauge group, but, because of the absence of a corresponding 'magnetic' gauge group, there is no 'duality' symmetry between electric and magnetic quantities. However, for a class of solutions to these equations, which includes all known point electric and magnetic monopole constructions, there is shown to exist an equivalent description based on a magnetic, rather than electric, gauge group. The gauge potentials in general are singular on strings extending from the particle position to infinity, but it is shown that the observables are without string singularities, and that the theory is Lorentz invariant, provided a charge quantization condition is satisfied. This condition, deduced from a stability analysis, is necessary for the consistency of the classical non-Abelian theory, in contrast to the Abelian case, where such a condition is necessary only for the consistency of the quantum theory. It is also shown that in the classical theory the strings cannot be removed by gauge transformations, as they sometimes can be in the quantum theory. (Auth.)

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)

Gravitational waves from quasicircular black-hole binaries in dynamical Chern-Simons gravity.

Science.gov (United States)

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.

Euler–Chern–Simons gravity from Lovelock–Born–Infeld gravity

OpenAIRE

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.

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.

Non-Abelian tensor gauge fields and higher-spin extension of standard model

International Nuclear Information System (INIS)

Savvidy, G.

2006-01-01

We suggest an extension of the gauge principle which includes non-Abelian tensor gauge fields. The invariant Lagrangian is quadratic in the field strength tensors and describes interaction of charged tensor gauge bosons of arbitrary large integer spin 1,2,l. Non-Abelian tensor gauge fields can be viewed as a unique gauge field with values in the infinite-dimensional current algebra associated with compact Lie group. The full Lagrangian exhibits also enhanced local gauge invariance with double number of gauge parameters which allows to eliminate all negative norm states of the nonsymmetric second-rank tensor gauge field, which describes therefore two polarizations of helicity-two massless charged tensor gauge boson and the helicity-zero ''axion'' The geometrical interpretation of the enhanced gauge symmetry with double number of gauge parameters is not yet known. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

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

Initial value formulation of dynamical Chern-Simons gravity

Science.gov (United States)

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.

The Weyl non-Abelian gauge field and the Thomas precession

International Nuclear Information System (INIS)

Barbashov, B.M.; Pestov, A.B.

1998-01-01

The connection between the Fermi-Walker transport and the Weyl non-Abelian gauge field is established. A theoretical possibility of detecting the Weyl gauge field caused by the Thomas precession of a gyroscope is discussed

The chiral bosonization in non-Abelian gauge theories

International Nuclear Information System (INIS)

Andrianov, A.A.; Novozhilov, Y.

1985-01-01

The chiral bosonization in non-Abelian gauge theories is described starting directly from the QCD functional. For a given mass scale Λ, the QCD may be equivalently represented by colour chiral fields, gauge fields and high energy fermions. The effective action for colour chiral fields may admit the existence of a colour Skyrmion-boson with the baryon number 2/3. (author)

Possible daily and seasonal variations in quantum interference induced by Chern-Simons gravity.

Science.gov (United States)

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.

Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields

Science.gov (United States)

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

International Nuclear Information System (INIS)

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

Comment on the Adler-Bardeen theorem in non-Abelian gauge theories

International Nuclear Information System (INIS)

Fujikawa, Kazuo.

1981-09-01

It is pointed out that the constructive proof of the Adler-Bardeen theorem for the chiral and scale (counting identity) anomalies in non-Abelian gauge theories proceeds just as in the spinor electrodynamics, although several interesting features characteristic of non-Abelian theories appear. (author)

Appearance of gauge structure in simple dynamical systems

Science.gov (United States)

Wilczek, F.; Zee, A.

1984-01-01

By generalizing a construction of Berry and Simon, it is shown that non-Abelian gauge fields arise in the adiabatic development of simple quantum mechanical systems. Characteristics of the gauge fields are related to energy splittings, which may be observable in real systems. Similar phenomena are found for suitable classical systems.

Non-Abelian gauge field theory in scale relativity

International Nuclear Information System (INIS)

Nottale, Laurent; Celerier, Marie-Noeelle; Lehner, Thierry

2006-01-01

Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a coupling is expected between displacements in the fractal space-time and the transformations of these scale variables. In previous works, an Abelian gauge theory (electromagnetism) has been derived as a consequence of this coupling for global dilations and/or contractions. We consider here more general transformations of the scale variables by taking into account separate dilations for each of them, which yield non-Abelian gauge theories. We identify these transformations with the usual gauge transformations. The gauge fields naturally appear as a new geometric contribution to the total variation of the action involving these scale variables, while the gauge charges emerge as the generators of the scale transformation group. A generalized action is identified with the scale-relativistic invariant. The gauge charges are the conservative quantities, conjugates of the scale variables through the action, which find their origin in the symmetries of the ''scale-space.'' We thus found in a geometric way and recover the expression for the covariant derivative of gauge theory. Adding the requirement that under the scale transformations the fermion multiplets and the boson fields transform such that the derived Lagrangian remains invariant, we obtain gauge theories as a consequence of scale symmetries issued from a geometric space-time description

Aspects Topologiques de la Theorie des Champs et leurs Applications

Science.gov (United States)

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

Classical solutions of Yang-Mills-Chern-Simons theory in 2+1 dimensions: A quasi-linear superposition

International Nuclear Information System (INIS)

Teh, R.

1993-06-01

We pointed out that there exists a critical frequency of oscillation for the vortex-like solution above which the system switches to the fields of an alternating current inside a solenoid. We also show the existence a non-abelian gauge for which the fields can alternate periodically in space between the abelian fields and another abelian (or non-abelian) field pointing in a different isospin space direction. The solution discussed here are real, zero-action Minkowski space configurations. (author). 18 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.)

Massive Abelian gauge fields coupled with nonconserved currents

International Nuclear Information System (INIS)

Nakazato, Hiromichi; Namiki, Mikio; Yamanaka, Yoshiya; Yokoyama, Kan-ichi.

1985-04-01

A massive Abelian gauge field coupled with a nonconserved mass-changing current is described within the framework of canonical quantum theory with indefinite metric. In addition to the conventional Lagrange multiplier fields, another ghost field is introduced to preserve gauge invariance and unitarity of a physical S-matrix in the case of the nonconserved current. The renormalizability of the theory is explicitly shown in the sense of superpropagator approach for nonpolynomial Lagrangian theories. (author)

Gauge invariance of color confinement due to the dual Meissner effect caused by Abelian monopoles

International Nuclear Information System (INIS)

Suzuki, Tsuneo; Hasegawa, Masayasu; Ishiguro, Katsuya; Koma, Yoshiaki; Sekido, Toru

2009-01-01

The mechanism of non-Abelian color confinement is studied in SU(2) lattice gauge theory in terms of the Abelian fields and monopoles extracted from non-Abelian link variables without adopting gauge fixing. First, the static quark-antiquark potential and force are computed with the Abelian and monopole Polyakov loop correlators, and the resulting string tensions are found to be identical to the non-Abelian string tension. These potentials also show the scaling behavior with respect to the change of lattice spacing. Second, the profile of the color-electric field between a quark and an antiquark is investigated with the Abelian and monopole Wilson loops. The color-electric field is squeezed into a flux tube due to monopole supercurrent with the same Abelian color direction. The parameters corresponding to the penetration and coherence lengths show the scaling behavior, and the ratio of these lengths, i.e., the Ginzburg-Landau parameter, indicates that the vacuum type is near the border of the type 1 and type 2 (dual) superconductors. These results are summarized in which the Abelian fundamental charge defined in an arbitrary color direction is confined inside a hadronic state by the dual Meissner effect. As the color-neutral state in any Abelian color direction corresponds to the physical color-singlet state, this effect explains non-Abelian color confinement and supports the existence of a gauge-invariant mechanism of color confinement due to the dual Meissner effect caused by Abelian monopoles.

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.

A study of the path-integral quantization of Abelian gauge theories when no explicit gauge-fixing term is included in the bilinear part of the gauge-field action

International Nuclear Information System (INIS)

Phillips, S.

1985-01-01

The mathematical problem of inverting the operator Δ x μν ≡ g μν g αβ δ x α δ x β -δ x μ δ x ν , as it arises in the path-integral quantization of an Abelian gauge theory, such as quantum electrodynamics, when no gauge-fixing Lagrangian field density is included, is studied in this article. Making use of the fact that the Schwinger source functions, which are introduced for the purpose of generating Green's functions, are free of divergence, a result that follows from the conversion of the exponentiated action into a Gaussian form, the apparently noninvertible partial differential equation, Δ x μν L ν (x) J μ (x), can, by the addition and subsequent subtraction of terms containing the divergence of the source function, be cast into a form that does possess a Green's function solution. The gauge-field propagator is the same as that obtained by the conventional technique, which involves gauge fixing when the gauge parameter, α, is set equal to one. Such an analysis suggests also that, provided the effect of fictitious particles that propagate only in closed loops are included for the study of Green's functions in non-Abelian gauge theories in Landau-type gauges, then, in quantizing either Abelian gauge theories or non-Abelian gauge theories in this generic kind of gauge, it is not necessary to add an explicit gauge-fixing term to the bilinear part of the gauge-field action

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.

Flavored gauge mediation with discrete non-Abelian symmetries

Science.gov (United States)

Everett, Lisa L.; Garon, Todd S.

2018-05-01

We explore the model building and phenomenology of flavored gauge-mediation models of supersymmetry breaking in which the electroweak Higgs doublets and the S U (2 ) messenger doublets are connected by a discrete non-Abelian symmetry. The embedding of the Higgs and messenger fields into representations of this non-Abelian Higgs-messenger symmetry results in specific relations between the Standard Model Yukawa couplings and the messenger-matter Yukawa interactions. Taking the concrete example of an S3 Higgs-messenger symmetry, we demonstrate that, while the minimal implementation of this scenario suffers from a severe μ /Bμ problem that is well known from ordinary gauge mediation, expanding the Higgs-messenger field content allows for the possibility that μ and Bμ can be separately tuned, allowing for the possibility of phenomenologically viable models of the soft supersymmetry-breaking terms. We construct toy examples of this type that are consistent with the observed 125 GeV Higgs boson mass.

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

(Non-)Abelian Kramers-Wannier duality and topological field theory

CERN Document Server

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.

Large N non-perturbative effects in N=4 superconformal Chern-Simons theories

International Nuclear Information System (INIS)

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.

Non-Abelian black holes in D=5 maximal gauged supergravity

International Nuclear Information System (INIS)

Cvetic, M.; Lue, H.; Pope, C. N.

2010-01-01

We investigate static non-Abelian black hole solutions of anti-de Sitter (AdS) Einstein-Yang-Mills-dilaton gravity, which is obtained as a consistent truncation of five-dimensional maximal gauged supergravity. If the dilaton is (consistently) set to zero, the remaining equations of motion, with a spherically-symmetric ansatz, may be derived from a superpotential. The associated first-order equations admit an explicit solution supported by a non-Abelian SU(2) gauge potential, which has a logarithmically growing mass term. In an extremal limit the horizon geometry becomes AdS 2 xS 3 . If the dilaton is also excited, the equations of motion cannot easily be solved explicitly, but we obtain the asymptotic form of the more general non-Abelian black holes in this case. An alternative consistent truncation, in which the Yang-Mills fields are set to zero, also admits a description in terms of a superpotential. This allows us to construct explicit wormhole solutions (neutral spherically-symmetric domain walls). These solutions may be generalized to dimensions other than five.

Stochastic quantization of topological field theory: generalized Langevin equation with memory kernel

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)

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.)

The static quark potential from the gauge independent Abelian decomposition

Energy Technology Data Exchange (ETDEWEB)

Cundy, Nigel, E-mail: ndcundy@gmail.com [Lattice Gauge Theory Research Center, FPRD, and CTP, Department of Physics & Astronomy, Seoul National University, Seoul 151-747 (Korea, Republic of); Cho, Y.M. [Administration Building 310-4, Konkuk University, Seoul 143-701 (Korea, Republic of); Department of Physics & Astronomy, Seoul National University, Seoul 151-747 (Korea, Republic of); Lee, Weonjong; Leem, Jaehoon [Lattice Gauge Theory Research Center, FPRD, and CTP, Department of Physics & Astronomy, Seoul National University, Seoul 151-747 (Korea, Republic of)

2015-06-15

We investigate the relationship between colour confinement and the gauge independent Cho–Duan–Ge Abelian decomposition. The decomposition is defined in terms of a colour field n; the principle novelty of our study is that we have used a unique definition of this field in terms of the eigenvectors of the Wilson Loop. This allows us to establish an equivalence between the path-ordered integral of the non-Abelian gauge fields and an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. We circumvent path ordering without requiring an additional path integral. By using Stokes' theorem, we can compute the Wilson Loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by certain structures, which occur when one of the quantities parametrising the colour field n winds itself around a non-analyticity in the colour field. If they exist, these structures will lead to an area law scaling for the Wilson Loop and provide a mechanism for quark confinement. Unlike most studies of confinement using the Abelian decomposition, we do not rely on a dual-Meissner effect to create the inter-quark potential. We search for these structures in quenched lattice QCD. We perform the Abelian decomposition, and compare the electric and magnetic fields with the patterns expected theoretically. We find that the restricted field strength is dominated by objects which may be peaks of a single lattice spacing in size or extended string-like lines of electromagnetic flux. The objects are not isolated monopoles, as they generate electric fields in addition to magnetic fields, and the fields are not spherically symmetric, but may be either caused by a monopole/anti-monopole condensate, some other types of topological objects, or a combination of these. Removing these peaks removes the area law scaling of the string tension, suggesting that they are

The static quark potential from the gauge independent Abelian decomposition

Directory of Open Access Journals (Sweden)

Nigel Cundy

2015-06-01

Full Text Available We investigate the relationship between colour confinement and the gauge independent Cho–Duan–Ge Abelian decomposition. The decomposition is defined in terms of a colour field n; the principle novelty of our study is that we have used a unique definition of this field in terms of the eigenvectors of the Wilson Loop. This allows us to establish an equivalence between the path-ordered integral of the non-Abelian gauge fields and an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. We circumvent path ordering without requiring an additional path integral. By using Stokes' theorem, we can compute the Wilson Loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by certain structures, which occur when one of the quantities parametrising the colour field n winds itself around a non-analyticity in the colour field. If they exist, these structures will lead to an area law scaling for the Wilson Loop and provide a mechanism for quark confinement. Unlike most studies of confinement using the Abelian decomposition, we do not rely on a dual-Meissner effect to create the inter-quark potential.We search for these structures in quenched lattice QCD. We perform the Abelian decomposition, and compare the electric and magnetic fields with the patterns expected theoretically. We find that the restricted field strength is dominated by objects which may be peaks of a single lattice spacing in size or extended string-like lines of electromagnetic flux. The objects are not isolated monopoles, as they generate electric fields in addition to magnetic fields, and the fields are not spherically symmetric, but may be either caused by a monopole/anti-monopole condensate, some other types of topological objects, or a combination of these. Removing these peaks removes the area law scaling of the string tension, suggesting that

The static quark potential from the gauge independent Abelian decomposition

Science.gov (United States)

Cundy, Nigel; Cho, Y. M.; Lee, Weonjong; Leem, Jaehoon

2015-06-01

We investigate the relationship between colour confinement and the gauge independent Cho-Duan-Ge Abelian decomposition. The decomposition is defined in terms of a colour field n; the principle novelty of our study is that we have used a unique definition of this field in terms of the eigenvectors of the Wilson Loop. This allows us to establish an equivalence between the path-ordered integral of the non-Abelian gauge fields and an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. We circumvent path ordering without requiring an additional path integral. By using Stokes' theorem, we can compute the Wilson Loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by certain structures, which occur when one of the quantities parametrising the colour field n winds itself around a non-analyticity in the colour field. If they exist, these structures will lead to an area law scaling for the Wilson Loop and provide a mechanism for quark confinement. Unlike most studies of confinement using the Abelian decomposition, we do not rely on a dual-Meissner effect to create the inter-quark potential. We search for these structures in quenched lattice QCD. We perform the Abelian decomposition, and compare the electric and magnetic fields with the patterns expected theoretically. We find that the restricted field strength is dominated by objects which may be peaks of a single lattice spacing in size or extended string-like lines of electromagnetic flux. The objects are not isolated monopoles, as they generate electric fields in addition to magnetic fields, and the fields are not spherically symmetric, but may be either caused by a monopole/anti-monopole condensate, some other types of topological objects, or a combination of these. Removing these peaks removes the area law scaling of the string tension, suggesting that they are responsible for

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

Abelian projection on the torus for general gauge groups

International Nuclear Information System (INIS)

Ford, C.; Tok, T.; Wipf, A.

1999-01-01

We consider Yang-Mills theories with general gauge groups G and twists of the four-torus. We find consistent boundary conditions for gauge fields in all instanton sectors. An extended abelian projection with respect to the Polyakov loop operator is presented, where A 0 is independent of time and in the Cartan subalgebra. Fundamental domains for the gauge fixed A 0 are constructed for arbitrary gauge groups. In the sectors with non-vanishing instanton number such gauge fixings are necessarily singular. The singularities can be restricted to Dirac strings joining magnetically charged defects. The magnetic charges of these monopoles take their values in the co-root lattice of the gauge group. We relate the magnetic charges of the defects and the windings of suitable Higgs fields about these defects to the instanton number

Decoupling, effective Lagrangian, and gauge hierarchy in spontaneously broken non-Abelian gauge theories

International Nuclear Information System (INIS)

Kazama, Y.; Yao, Y.

1982-01-01

In spontaneously broken non-Abelian gauge theories which admit gauge hierarchy at the tree level, we show, to all orders in perturbation theory, that (i) the superheavy particles decouple from the light sector at low energies, (ii) an effective low-energy renormalizable theory emerges together with appropriate counterterms, and (iii) the gauge hierarchy can be consistently maintained in the presence of radiative corrections. These assertions are explicitly demonstrated for O(3) gauge theory with two triplets of Higgs particles in a manner easily applicable to more realistic grand unified theories. Furthermore, as a by-product of our analysis, we obtain a systematic method of computing the parameters of the effective low-energy theory via renormalization-group equations to any desired accuracy

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

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

Off-diagonal mass generation for Yang-Mills theories in the maximal Abelian gauge

International Nuclear Information System (INIS)

Dudal, D.; Verschelde, H.; Sarandy, M.S.

2007-01-01

We investigate a dynamical mass generation mechanism for the off-diagonal gluons and ghosts in SU(N) Yang-Mills theories, quantized in the maximal Abelian gauge. Such a mass can be seen as evidence for the Abelian dominance in that gauge. It originates from the condensation of a mixed gluon-ghost operator of mass dimension two, which lowers the vacuum energy. We construct an effective potential for this operator by a combined use of the local composite operators technique with algebraic renormalization and we discuss the gauge parameter independence of the results. We also show that it is possible to connect the vacuum energy, due to the mass dimension two condensate discussed here, with the non-trivial vacuum energy originating from the condensate 2 μ >, which has attracted much attention in the Landau gauge. (author)

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.)

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.

Constant self-dual Abelian gauge fields and fermions in SU(2) gauge theory

International Nuclear Information System (INIS)

Kay, D.; Parthasarathy, R.; Viswanathan, K.S.

1983-01-01

Fermion one-loop corrections to the effective action in a self-dual Abelian background field are calculated for an SU(2) gauge theory. It is found that these corrections for massless fermions tend to destabilize the vacuum. The quantitative and qualitative features of such corrections for the case of massive fermions are discussed

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)

Scalar formalism for non-Abelian gauge theory

International Nuclear Information System (INIS)

Hostler, L.C.

1986-01-01

The gauge field theory of an N-dimensional multiplet of spin- 1/2 particles is investigated using the Klein--Gordon-type wave equation ]Pi x (1+isigma) x Pi+m 2 ]Phi = 0, Pi/sub μ/equivalentpartial/partialix/sub μ/-eA/sub μ/, investigated before by a number of authors, to describe the fermions. Here Phi is a 2 x 1 Pauli spinor, and sigma repesents a Lorentz spin tensor whose components sigma/sub μ//sub ν/ are ordinary 2 x 2 Pauli spin matrices. Feynman rules for the scalar formalism for non-Abelian gauge theory are derived starting from the conventional field theory of the multiplet and converting it to the new description. The equivalence of the new and the old formalism for arbitrary radiative processes is thereby established. The conversion to the scalar formalism is accomplished in a novel way by working in terms of the path integral representation of the generating functional of the vacuum tau-functions, tau(2,1, xxx 3 xxx)equivalent , where Psi/sub in/ is a Heisenberg operator belonging to a 4N x 1 Dirac wave function of the multiplet. The Feynman rules obtained generalize earlier results for the Abelian case of quantum electrodynamics

Criticality and novel quantum liquid phases in Ginzburg-Landau theories with compact and non-compact gauge fields

Energy Technology Data Exchange (ETDEWEB)

Smiseth, Jo

2005-07-01

The critical properties of three-dimensional U(1)-symmetric lattice gauge theories have been studied. The models apply to various physical systems such as insulating phases of strongly correlated electron systems as well as superconducting and superfluid states of liquid metallic hydrogen under extreme pressures. The thesis contains an introductory part and a collection of research papers of which seven are published works and one is submitted for publication. The outline of this thesis is as follows. In Chapter 2 the theory of phase transitions is discussed with emphasis on continuous phase transitions, critical phenomena and phase transitions in gauge theories. In the next chapter the phases of the abelian Higgs model are presented, and the critical phenomena are discussed. Furthermore, the multicomponent Ginzburg-Landau theory and the applications to liquid metallic hydrogen are presented. Chapter 4 contains an overview of the Monte Carlo integration scheme, including the Metropolis algorithm, error estimates, and re weighting techniques. This chapter is followed by the papers I-VIII. Paper I: Criticality in the (2+1)-Dimensional Compact Higgs Model and Fractionalized Insulators. Paper II: Phase structure of (2+1)-dimensional compact lattice gauge theories and the transition from Mott insulator to fractionalized insulator. Paper III: Compact U(1) gauge theories in 2+1 dimensions and the physics of low dimensional insulating materials. Paper IV: Phase structure of Abelian Chern-Simons gauge theories. Paper V: Critical Properties of the N-Color London Model. Paper VI: Field- and temperature induced topological phase transitions in the three-dimensional N-component London superconductor. Paper VII: Vortex Sublattice Melting in a Two-Component Superconductor. Paper VIII: Observation of a metallic superfluid in a numerical experiment (ml)

Renormalization of an abelian gauge theory in stochastic quantization

International Nuclear Information System (INIS)

Chaturvedi, S.; Kapoor, A.K.; Srinivasan, V.

1987-01-01

The renormalization of an abelian gauge field coupled to a complex scalar field is discussed in the stochastic quantization method. The super space formulation of the stochastic quantization method is used to derive the Ward Takahashi identities associated with supersymmetry. These Ward Takahashi identities together with previously derived Ward Takahashi identities associated with gauge invariance are shown to be sufficient to fix all the renormalization constants in terms of scaling of the fields and of the parameters appearing in the stochastic theory. (orig.)

On the SL(2,R) symmetry in Yang-Mills theories in the Landau, Curci-Ferrari and maximal abelian gauge

International Nuclear Information System (INIS)

Dudal, David; Verschelde, Henri; Rodino Lemes, Vitor Emanuel; Sarandy, Marcelo S.; Sorella, Silvio Paolo; Picariello, Marco

2002-01-01

The existence of a SL(2;R) symmetry is discussed in SU(N) Yang-Mills in the maximal abelian gauge. This symmetry, also present in the Landau and Curci-Ferrari gauge, ensures the absence of tachyons in the maximal abelian gauge. In all these gauges, SL(2;R) turns out to be dynamically broken by ghost condensates. (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

Maximal Abelian and Curci-Ferrari gauges in momentum subtraction at three loops

Science.gov (United States)

Bell, J. M.; Gracey, J. A.

2015-12-01

The vertex structure of QCD fixed in the maximal Abelian gauge (MAG) and Curci-Ferrari gauge is analyzed at two loops at the fully symmetric point for the 3-point functions corresponding to the three momentum subtraction (MOM) renormalization schemes. Consequently, the three-loop renormalization group functions are determined for each of these three schemes in each gauge using properties of the renormalization group equation.

Recursion rules for scattering amplitudes in non-Abelian gauge theories

International Nuclear Information System (INIS)

Kim, C.; Nair, V.P.

1997-01-01

We present a functional derivation of recursion rules for scattering amplitudes in a non-Abelian gauge theory in a form valid to arbitrary loop order. The tree-level and one-loop recursion rules are explicitly displayed. copyright 1997 The American Physical Society

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

Science.gov (United States)

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.

Topics in string theory

Science.gov (United States)

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.

Harada–Tsutsui gauge recovery procedure: From Abelian gauge anomalies to the Stueckelberg mechanism

International Nuclear Information System (INIS)

Lima, Gabriel Di Lemos Santiago

2014-01-01

Revisiting a path-integral procedure developed by Harada and Tsutsui for recovering gauge invariance from anomalous effective actions, it is shown that there are two ways to achieve gauge symmetry: one already presented by the authors, which is shown to preserve the anomaly in the sense of standard current conservation law, and another one which is anomaly-free, preserving current conservation. It is also shown that the application of the Harada–Tsutsui technique to other models which are not anomalous but do not exhibit gauge invariance allows the identification of the gauge invariant formulation of the Proca model, also done by the referred authors, with the Stueckelberg model, leading to the interpretation of the gauge invariant map as a generalization of the Stueckelberg mechanism. -- Highlights: • A gauge restoration technique from Abelian anomalous models is discussed. • It is shown that there is another way that leads to gauge symmetry restoration from such technique. • It is shown that the first gauge restoration preserves the anomaly, while the proposed second one is free from anomalies. • It is shown that the proposed gauge symmetry restoration can be identified with the Stueckelberg mechanism

Harada–Tsutsui gauge recovery procedure: From Abelian gauge anomalies to the Stueckelberg mechanism

Energy Technology Data Exchange (ETDEWEB)

Lima, Gabriel Di Lemos Santiago, E-mail: gabriellemos3@hotmail.com

2014-02-15

Revisiting a path-integral procedure developed by Harada and Tsutsui for recovering gauge invariance from anomalous effective actions, it is shown that there are two ways to achieve gauge symmetry: one already presented by the authors, which is shown to preserve the anomaly in the sense of standard current conservation law, and another one which is anomaly-free, preserving current conservation. It is also shown that the application of the Harada–Tsutsui technique to other models which are not anomalous but do not exhibit gauge invariance allows the identification of the gauge invariant formulation of the Proca model, also done by the referred authors, with the Stueckelberg model, leading to the interpretation of the gauge invariant map as a generalization of the Stueckelberg mechanism. -- Highlights: • A gauge restoration technique from Abelian anomalous models is discussed. • It is shown that there is another way that leads to gauge symmetry restoration from such technique. • It is shown that the first gauge restoration preserves the anomaly, while the proposed second one is free from anomalies. • It is shown that the proposed gauge symmetry restoration can be identified with the Stueckelberg mechanism.

Restoration of the local gauge symmetry and color confinement in non-Abelian gauge theories

International Nuclear Information System (INIS)

Hata, Hiroyuki

1982-01-01

Restoration of the local gauge symmetry and its connection to color confinement is investigated in non-Abelian gauge theories with covariant gauge fixing. We consider the Noether current J sub(μ,#betta#)sup(a) of the local gauge transformation with transformation functions #betta#sup(b)(x) linear in x sub(μ); #betta#sup(b)(x) = delta sup(ab)x sub(#betta#). This current is conserved only in the physical subspace of the state vector space and in perturbation theory contains a massless pole communicating to the gauge field. We define the local gauge symmetry restoration as the disappearance of this massless ''Goldstone'' pole from J sub(μ,#betta#)sup(a). The restoration condition is obtained and it coincides exactly with the color confinement criterion proposed earlier by Kugo and Ojima. Quarks and other colored particles are shown to be confined in the local gauge symmetry restored phase by using the Ward identities of J sub(μ,#betta#)sup(a). (author)

Refined 3d-3d correspondence

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.

On the gauge invariant and topological nature of the localization determining the Quantum Hall Effect plateaus

CERN Document Server

Cabo-Montes de Oca, Alejandro

2002-01-01

It is shown how the electromagnetic response of 2DEG under Quantum Hall Effect regime, characterized by the Chern-Simons topological action, transforms the sample impurities and defects in charge-reservoirs that stabilize the Hall conductivity plateaus. The results determine the basic dynamical origin of the singular properties of localization under the occurrence of the Quantum Hall Effect obtained in the pioneering works of Laughlin and of Joynt and Prange, by means of a gauge invariance argument and a purely electronic analysis, respectively. The common intuitive picture of electrons moving along the equipotential lines gets an analytical realization through the Chern-Simons current and charge densities.

Study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge

International Nuclear Information System (INIS)

Capri, M.A.L.; Guimaraes, M.S.; Lemes, V.E.R.; Sorella, S.P.; Tedesco, D.G.

2014-01-01

A study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge is presented in the case of the gauge group SU(2) and for different Euclidean space–time dimensions. Explicit examples of classes of normalizable zero modes and corresponding gauge field configurations are constructed by taking into account two boundary conditions, namely: (i) the finite Euclidean Yang–Mills action, (ii) the finite Hilbert norm. -- Highlights: •We study the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge. •For d=2 we obtain solutions with finite action but not finite Hilbert norm. •For d=3,4 we obtain solutions with finite action and finite Hilbert norm. •These results can be compared with those previously obtained in the Landau gauge

Renormalization of non-abelian gauge theories in curved space-time

International Nuclear Information System (INIS)

Freeman, M.D.

1984-01-01

We use indirect, renormalization group arguments to calculate the gravitational counterterms needed to renormalize an interacting non-abelian gauge theory in curved space-time. This method makes it straightforward to calculate terms in the trace anomaly which first appear at high order in the coupling constant, some of which would need a 4-loop calculation to find directly. The role of gauge invariance in the theory is considered, and we discuss briefly the effect of using coordinate-dependent gauge-fixing terms. We conclude by suggesting possible applications of this work to models of the very early universe

On a stochastic process associated to non-abelian gauge fields

International Nuclear Information System (INIS)

Vilela Mendes, R.

1989-01-01

A stochastic process is constructed from a ground state measure that generalizes to non-abelian fields the ground state of abelian (free) gauge fields without fermions. Using a latticized version one shows how the process leads to a well-defined quantum theory in the Schroedinger representation. An analysis of the qualitative behaviour of the theory seems to imply a quasi-free behaviour at short distances and a maximally disordered field strength configuration for the low-momentum component of the ground state. Scaling relations for the mass gap are inferred from the theory of small random perturbations of dynamical systems. (orig.)

Taming the conformal zoo

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.)

On entanglement entropy in non-Abelian lattice gauge theory and 3D quantum gravity

Energy Technology Data Exchange (ETDEWEB)

Delcamp, Clement [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada); Department of Physics & Astronomy and Guelph-Waterloo Physics Institute, University of Waterloo,200 University Avenue West, Waterloo, Ontario N2L 3G1 (Canada); Dittrich, Bianca; Riello, Aldo [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada)

2016-11-18

Entanglement entropy is a valuable tool for characterizing the correlation structure of quantum field theories. When applied to gauge theories, subtleties arise which prevent the factorization of the Hilbert space underlying the notion of entanglement entropy. Borrowing techniques from extended topological field theories, we introduce a new definition of entanglement entropy for both Abelian and non-Abelian gauge theories. Being based on the notion of excitations, it provides a completely relational way of defining regions. Therefore, it naturally applies to background independent theories, e.g. gravity, by circumventing the difficulty of specifying the position of the entangling surface. We relate our construction to earlier proposals and argue that it brings these closer to each other. In particular, it yields the non-Abelian analogue of the ‘magnetic centre choice’, as obtained through an extended-Hilbert-space method, but applied to the recently introduced fusion basis for 3D lattice gauge theories. We point out that the different definitions of entanglement entropy can be related to a choice of (squeezed) vacuum state.

Quest for Casimir repulsion between Chern-Simons surfaces

Science.gov (United States)

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.

Gauge invariance and the effective potential: the Abelian Higgs model

International Nuclear Information System (INIS)

Ramaswamy, S.

1995-01-01

The gauge invariance of the effective potential in the Abelian Higgs model is examined. The Nielsen identities, which ensure gauge independence of the effective potential and other physical quantities, are shown to hold at finite temperature and in the presence of the chemical potential. It is also shown that, as a consequence of the Nielsen identities, the standard order parameter for symmetry breaking, namely the scalar field vacuum expectation value, has a non-zero parametric dependence on the gauge choice employed. These are then verified to one loop at finite temperature. High-temperature symmetry breaking is considered. In the leading high-temperature limit, the potential agrees with the previous calculations. (orig.)

Relative entropy, mixed gauge-gravitational anomaly and causality

Energy Technology Data Exchange (ETDEWEB)

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.

Thin accretion disk signatures in dynamical Chern-Simons-modified gravity

International Nuclear Information System (INIS)

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.

Self-dual configurations in Abelian Higgs models with k-generalized gauge field dynamics

Energy Technology Data Exchange (ETDEWEB)

Casana, R.; Cavalcante, A. [Departamento de Física, Universidade Federal do Maranhão,65080-805, São Luís, Maranhão (Brazil); Hora, E. da [Departamento de Física, Universidade Federal do Maranhão,65080-805, São Luís, Maranhão (Brazil); Coordenadoria Interdisciplinar de Ciência e Tecnologia, Universidade Federal do Maranhão,65080-805, São Luís, Maranhão (Brazil)

2016-12-14

We have shown the existence of self-dual solutions in new Maxwell-Higgs scenarios where the gauge field possesses a k-generalized dynamic, i.e., the kinetic term of gauge field is a highly nonlinear function of F{sub μν}F{sup μν}. We have implemented our proposal by means of a k-generalized model displaying the spontaneous symmetry breaking phenomenon. We implement consistently the Bogomol’nyi-Prasad-Sommerfield formalism providing highly nonlinear self-dual equations whose solutions are electrically neutral possessing total energy proportional to the magnetic flux. Among the infinite set of possible configurations, we have found families of k-generalized models whose self-dual equations have a form mathematically similar to the ones arising in the Maxwell-Higgs or Chern-Simons-Higgs models. Furthermore, we have verified that our proposal also supports infinite twinlike models with |ϕ|{sup 4}-potential or |ϕ|{sup 6}-potential. With the aim to show explicitly that the BPS equations are able to provide well-behaved configurations, we have considered a test model in order to study axially symmetric vortices. By depending of the self-dual potential, we have shown that the k-generalized model is able to produce solutions that for long distances have a exponential decay (as Abrikosov-Nielsen-Olesen vortices) or have a power-law decay (characterizing delocalized vortices). In all cases, we observe that the generalization modifies the vortex core size, the magnetic field amplitude and the bosonic masses but the total energy remains proportional to the quantized magnetic flux.

Effective Chern-Simons actions of particles coupled to 3D gravity

Science.gov (United States)

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.

Finite-size effect of the dyonic giant magnons in N=6 super Chern-Simons theory

International Nuclear Information System (INIS)

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.

Analytical results for Abelian projection

International Nuclear Information System (INIS)

Ogilivie, Michael C.

1999-01-01

Analytic methods for Abelian projection are developed, and a number of results related to string tension measurements are obtained. It is proven that even without gauge fixing, Abelian projection yields string tensions of the underlying non-Abelian theory. Strong arguments are given for similar results in the case where gauge fixing is employed. The subgroup used for projection need only contain the center of the gauge group, and need not be Abelian. While gauge fixing is shown to be in principle unnecessary for the success of Abelian projection, it is computationally advantageous for the same reasons that improved operators, e.g., the use of fat links, are advantageous in Wilson loop measurements

Emergent Abelian Gauge Fields from Noncommutative Gravity

Directory of Open Access Journals (Sweden)

Allen Stern

2010-02-01

Full Text Available We construct exact solutions to noncommutative gravity following the formulation of Chamseddine and show that they are in general accompanied by Abelian gauge fields which are first order in the noncommutative scale. This provides a mechanism for generating cosmological electromagnetic fields in an expanding space-time background, and also leads to multipole-like fields surrounding black holes. Exact solutions to noncommutative Einstein-Maxwell theory can give rise to first order corrections to the metric tensor, as well as to the electromagnetic fields. This leads to first order shifts in the horizons of charged black holes.

Vortices in superconductors from Lorentz violation

International Nuclear Information System (INIS)

Belich, H.; Orlando, M.T.D.; Costa-Soares, T.; Helayel-Neto, J.A.

2004-01-01

We start from a Lorentz non-invariant Abelian-Higgs model in 1+3 dimensions, and carry out its dimensional reduction to D = 1 + 2. The planar model resulting thereof is composed by a Maxwell-Chern-Simons-Proca gauge sector, a massive scalar sector, and a mixing term (involving the fixed background, v μ ) that realizes Lorentz violation for the reduced model. Vortex type solutions of the planar model are investigated in a superconducting environment . Our vortex solutions are electrically charged and exhibit a screened electric field. (author)

Non-Abelian vortices in N=1* gauge theory

International Nuclear Information System (INIS)

Markov, V.; Marshakov, A.; Yung, A.

2005-01-01

We consider the N=1* supersymmetric SU(2) gauge theory and demonstrate that the Z2 vortices in this theory acquire orientational zero modes, associated with the rotation of magnetic flux inside SU(2) group, and turn into the non-Abelian strings, when the masses of all chiral fields become equal. These non-Abelian strings are not BPS-saturated. We study the effective theory on the string world sheet and show that it is given by two-dimensional non-supersymmetric O(3) sigma model. The confined 't Hooft-Polyakov monopole is seen as a junction of the Z2-string and anti-string, and as a kink in the effective world sheet sigma model. We calculate its mass and show that besides the four-dimensional confinement of monopoles, they are also confined in the two-dimensional theory: the monopoles stick to anti-monopoles to form the meson-like configurations on the strings they are attached to

Construction of quantized gauge fields: continuum limit of the Abelian Higgs model in two dimensions

International Nuclear Information System (INIS)

Seiler, E.

1981-01-01

The author proves the existence of the continuum limit of the two-dimensional Higgs model for two cases: External gauge fields that are Hoelder continuous and may be non-Abelian, and the fully quantized Abelian model. In the latter case all Wightman axioms are verified except clustering. Important ingredients are a universal diamagnetic bound and correlation inequalities. (Auth.)

Twisted boundary conditions: a non-perturbative probe for pure non-abelian gauge theories

International Nuclear Information System (INIS)

Baal, P. van.

1984-01-01

In this thesis the author describes a pure non-abelian gauge theory on the hypertorus with gauge group SU(N). To test the flux tube picture he has studied the large distance limit of this theory, leading to a large coupling constant. To tackle this problem, he describes two approaches, in both of which twisted boundary conditions play an important role. (Auth.)

New Applications of Resummation in Non-Abelian Gauge Theories: QED-QCD Exponentiation for LHC Physics, IR-Improved DGLAP Theory and Resummed Quantum Gravity

International Nuclear Information System (INIS)

Ward, B.F.L.

2006-01-01

We present the elements of three applications of resummation methods in non-Abelian gauge theories: (1), QED-QCD exponentiation and shower/ME matching for LHC physics; (2), IR improvement of DGLAP theory; (3), resummed quantum gravity and the final state of Hawking radiation. In all cases, the extension of the YFS approach, originally introduced for Abelian gauge theory, to non-Abelian gauge theories, QCD and quantum general relativity, leads to new results and solutions which we briefly summarize

Chaos, scaling and existence of a continuum limit in classical non-Abelian lattice gauge theory

International Nuclear Information System (INIS)

Nielsen, H.B.; Rugh, H.H.; Rugh, S.E.

1996-01-01

We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a open-quote no goclose quotes for simulating the original continuum classical gauge fields over a long time span since there is a never ending dynamical cascading towards the ultraviolet. We note that the temporal chaotic properties of the original continuum gauge fields and the lattice gauge system have entirely different scaling properties thereby emphasizing that they are entirely different dynamical systems which have only very little in common. Considered as a statistical system in its own right the lattice gauge system in a situation where it has reached equilibrium comes closest to what could be termed a open-quotes continuum limitclose quotes in the limit of very small energies (weak non-linearities). We discuss the lattice system both in the limit for small energies and in the limit of high energies where we show that there is a saturation of the temporal chaos as a pure lattice artifact. Our discussion focuses not only on the temporal correlations but to a large extent also on the spatial correlations in the lattice system. We argue that various conclusions of physics have been based on monitoring the non-Abelian lattice system in regimes where the fields are correlated over few lattice units only. This is further evidenced by comparison with results for Abelian lattice gauge theory. How the real time simulations of the classical lattice gauge theory may reach contact with the real time evolution of (semi-classical aspects of) the quantum gauge theory (e.g. Q.C.D.) is left an important question to be further examined

'Symmetry dictates interaction'. For the jubilee of the non-abelian gauge fields

International Nuclear Information System (INIS)

Li Huazhong

2004-01-01

The article is written for the Jubilee, 50 years after the birth of non-abelian gauge field theory which was proposed by C.N. yang and R. Mills in 1954. The main ideas initiated in the paper and great influences are briefly outlined

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.)

(Anti-)chiral superfield approach to interacting Abelian 1-form gauge theories: Nilpotent and absolutely anticommuting charges

Science.gov (United States)

Chauhan, B.; Kumar, S.; Malik, R. P.

2018-02-01

We derive the off-shell nilpotent (fermionic) (anti-)BRST symmetry transformations by exploiting the (anti-)chiral superfield approach (ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism for the interacting Abelian 1-form gauge theories where there is a coupling between the U(1) Abelian 1-form gauge field and Dirac as well as complex scalar fields. We exploit the (anti-)BRST invariant restrictions on the (anti-)chiral superfields to derive the fermionic symmetries of our present D-dimensional Abelian 1-form gauge theories. The novel observation of our present investigation is the derivation of the absolute anticommutativity of the nilpotent (anti-)BRST charges despite the fact that our ordinary D-dimensional theories are generalized onto the (D,1)-dimensional (anti-) chiral super-submanifolds (of the general (D,2)-dimensional supermanifold) where only the (anti-)chiral super expansions of the (anti-)chiral superfields have been taken into account. We also discuss the nilpotency of the (anti-)BRST charges and (anti-)BRST invariance of the Lagrangian densities of our present theories within the framework of ACSA to BRST formalism.

Approche Kaluza-Klein et Supersymetrie de Jauge

Science.gov (United States)

Pare, Jean-Pierre

trajectories of spinning particles. It is interesting to mention how this gauge -supersymmetry is introduced in the dynamics. It arises by choosing the unique metric connection on the principal bundle with torsion given by the Chern-Simons 3-form. We then proceed to extend these formulations for spinning strings. We present Lagrangian and Hamiltonian gauge-supersymmetric formulations in a superloop space setting. The same connection corresponding to the Chern -Simons 3-form is used here. Equations of motion are derived and discussed. In the appendix, we discuss the effect of using this connection in a non-Abelian Kaluza-Klein field theory. Using the same connection, we present a non-Abelian Kaluza-Klein approach leading to a zero cosmological constant.

Anomalous commutator of gauge group generators in a non-Abelian chiral theory

International Nuclear Information System (INIS)

Jo, S.

1985-01-01

This paper discusses commutators among non-Abelian fermion currents that are calculated using the BJL limit. It is observed that the gauge dependence of the fermion current with fixed canonical variables should be different from the covariant seagull in order to have correct anomalous commutators

Parity breaking signatures from a Chern-Simons coupling during inflation: the case of non-Gaussian gravitational waves

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.

Framing anomaly in the effective theory of the fractional quantum Hall effect.

Science.gov (United States)

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.

On the elimination of infinitesimal Gribov ambiguities in non-Abelian gauge theories

International Nuclear Information System (INIS)

Pereira, Antonio D.; Sobreiro, Rodrigo F.

2013-01-01

An alternative method to account for the Gribov ambiguities in gauge theories is presented. It is shown that, to eliminate Gribov ambiguities, at infinitesimal level, it is required to break the BRST symmetry in a soft manner. This can be done by introducing a suitable extra constraint that eliminates the infinitesimal Gribov copies. It is shown that the present approach is consistent with the well established known cases in the literature, i.e., the Landau and maximal Abelian gauges. The method is valid for gauges depending exclusively on the gauge field and is restricted to classical level. However, occasionally, we deal with quantum aspects of the technique, which are used to improve the results. (orig.)

Analytic study of the off-diagonal mass generation for Yang-Mills theories in the maximal Abelian gauge

International Nuclear Information System (INIS)

Dudal, D.; Verschelde, H.; Gracey, J.A.; Lemes, V.E.R.; Sobreiro, R.F.; Sorella, S.P.; Sarandy, M.S.

2004-01-01

We investigate a dynamical mass generation mechanism for the off-diagonal gluons and ghosts in SU(N) Yang-Mills theories, quantized in the maximal Abelian gauge. Such a mass can be seen as evidence for the Abelian dominance in that gauge. It originates from the condensation of a mixed gluon-ghost operator of mass dimension two, which lowers the vacuum energy. We construct an effective potential for this operator by a combined use of the local composite operators technique with the algebraic renormalization and we discuss the gauge parameter independence of the results. We also show that it is possible to connect the vacuum energy, due to the mass dimension-two condensate discussed here, with the nontrivial vacuum energy originating from the condensate μ 2 >, which has attracted much attention in the Landau gauge

Theory of Abelian projection

International Nuclear Information System (INIS)

Ogilvie, M.C.

1999-01-01

Analytic methods for Abelian projection are developed. A number of results are obtained related to string tension measurements. It is proven that even without gauge fixing, Abelian projection yields string tensions of the underlying non-Abelian theory. Strong arguments are given for similar results in the case where gauge fixing is employed. The methods used emphasize that the projected theory is derived from the underlying non-Abelian theory rather than vice versa. In general, the choice of subgroup used for projection is not very important, and need not be Abelian. While gauge fixing is shown to be in principle unnecessary for the success of Abelian projection, it is computationally advantageous for the same reasons that improved operators, e.g., the use of fat links, are advantageous in Wilson loop measurements. Two other issues, Casimir scaling and the conflict between projection and critical universality, are also discussed. copyright 1999 The American Physical Society

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.

Anomalous Lorentz and CPT violation

Science.gov (United States)

Klinkhamer, F. R.

2018-01-01

If there exists Lorentz and CPT violation in nature, then it is crucial to discover and understand the underlying mechanism. In this contribution, we discuss one such mechanism which relies on four-dimensional chiral gauge theories defined over a spacetime manifold with topology ℛ3 × S 1 and periodic spin structure for the compact dimension. It can be shown that the effective gauge-field action contains a local Chern-Simons-like term which violates Lorentz and CPT invariance. For arbitrary Abelian U(1) gauge fields with trivial holonomies in the compact direction, this anomalous Lorentz and CPT violation has recently been established perturbatively with a Pauli-Villars-type regularization and nonperturbatively with a lattice regularization based on Ginsparg-Wilson fermions.

Vortices and quark confinement in non-Abelian gauge theories

International Nuclear Information System (INIS)

Mandelstam, S.

1976-01-01

Non-Abelian vortices of the type proposed by Nielsen and Olesen are discussed. It is shown that the vortices must contain a single unit of quantized flux absorbed by a Dirac monopole at each end. The monopoles satisfy a confinement condition; if quark numbers are assigned to the monopoles, is is found that the model contains a natural explanation of quark confinement. The I-spin variables associated with the non-Abelian gauge field correspond to the colour degree freedom. An alternative model in which (colour) charges and monopoles are interchanged is also suggested. The Higgs field which breaks the degeneracy of the vacuum is replaced by an operator which creates monopoles of the type suggested by 't Hooft. In such a model colour might be confined. The investigations are at a very preliminary stage, but the model appears to offer a natural explanation of confinement without the explicit introduction of monopole fields. (Auth.)

The Hawking effect in abelian gauge theories

International Nuclear Information System (INIS)

Stephens, C.R.

1989-01-01

In an effort to compare and contrast gravity with other field theories an investigation is made into whether the Hawking effect is a peculiarly gravitational phenomenon. It is found that the effect exists for a particular background abelian gauge field configuration, as well as certain background gravitational field configurations. Specifically, pair production in a uniform electric field is shown to admit a thermal interpretation. In an effort to find out just what is singular about gravity it is found that the Hawking temperature characteristic of a particular gravitational field configuration is independent of the properties of the quantum fields propagating theorem, in direct contrast to the gauge field case. This implies that if the one loop approximation is to be valid the electric field must be ''cold'' relative to the energy scales set by the quantum fields. In gravity, however, because of the existence of a fundamental scale, the Planck length, the gravitational field can be ''hot'' or ''cold'' and a one loop approximation still remain valid. copyright 1989 Academic Press, Inc

Classical and quantum mechanics of non-abelian gauge fields

International Nuclear Information System (INIS)

Savvidy, G.K.

1984-01-01

Classical and quantum mechanics of non-abelian gauge fields are investigated both with and without spontaneous symmetry breaking. The fundamental subsystem (FS) of Yang-Mills classical mechanics (YMCM) is considered. It is shown to be a Kolmogorov K-system, and hence to have strong statistical properties. Integrable systems are also found, to which in terms of KAM theory Yang-Mills-Higgs classical mechanics (YMHCM) is close. Quantum-mechanical properties of the YM system and their relation to the problem of confinement are discussed. (orig.)

Worldlines and worldsheets for non-abelian lattice field theories: Abelian color fluxes and Abelian color cycles

Directory of Open Access Journals (Sweden)

Gattringer Christof

2018-01-01

Full Text Available We discuss recent developments for exact reformulations of lattice field theories in terms of worldlines and worldsheets. In particular we focus on a strategy which is applicable also to non-abelian theories: traces and matrix/vector products are written as explicit sums over color indices and a dual variable is introduced for each individual term. These dual variables correspond to fluxes in both, space-time and color for matter fields (Abelian color fluxes, or to fluxes in color space around space-time plaquettes for gauge fields (Abelian color cycles. Subsequently all original degrees of freedom, i.e., matter fields and gauge links, can be integrated out. Integrating over complex phases of matter fields gives rise to constraints that enforce conservation of matter flux on all sites. Integrating out phases of gauge fields enforces vanishing combined flux of matter-and gauge degrees of freedom. The constraints give rise to a system of worldlines and worldsheets. Integrating over the factors that are not phases (e.g., radial degrees of freedom or contributions from the Haar measure generates additional weight factors that together with the constraints implement the full symmetry of the conventional formulation, now in the language of worldlines and worldsheets. We discuss the Abelian color flux and Abelian color cycle strategies for three examples: the SU(2 principal chiral model with chemical potential coupled to two of the Noether charges, SU(2 lattice gauge theory coupled to staggered fermions, as well as full lattice QCD with staggered fermions. For the principal chiral model we present some simulation results that illustrate properties of the worldline dynamics at finite chemical potentials.

Worldlines and worldsheets for non-abelian lattice field theories: Abelian color fluxes and Abelian color cycles

Science.gov (United States)

Gattringer, Christof; Göschl, Daniel; Marchis, Carlotta

2018-03-01

We discuss recent developments for exact reformulations of lattice field theories in terms of worldlines and worldsheets. In particular we focus on a strategy which is applicable also to non-abelian theories: traces and matrix/vector products are written as explicit sums over color indices and a dual variable is introduced for each individual term. These dual variables correspond to fluxes in both, space-time and color for matter fields (Abelian color fluxes), or to fluxes in color space around space-time plaquettes for gauge fields (Abelian color cycles). Subsequently all original degrees of freedom, i.e., matter fields and gauge links, can be integrated out. Integrating over complex phases of matter fields gives rise to constraints that enforce conservation of matter flux on all sites. Integrating out phases of gauge fields enforces vanishing combined flux of matter-and gauge degrees of freedom. The constraints give rise to a system of worldlines and worldsheets. Integrating over the factors that are not phases (e.g., radial degrees of freedom or contributions from the Haar measure) generates additional weight factors that together with the constraints implement the full symmetry of the conventional formulation, now in the language of worldlines and worldsheets. We discuss the Abelian color flux and Abelian color cycle strategies for three examples: the SU(2) principal chiral model with chemical potential coupled to two of the Noether charges, SU(2) lattice gauge theory coupled to staggered fermions, as well as full lattice QCD with staggered fermions. For the principal chiral model we present some simulation results that illustrate properties of the worldline dynamics at finite chemical potentials.

Gravitationally induced zero modes of the Faddeev-Popov operator in the Coulomb gauge for Abelian gauge theories

Science.gov (United States)

Canfora, Fabrizio; Giacomini, Alex; Oliva, Julio

2010-08-01

It is shown that on curved backgrounds, the Coulomb gauge Faddeev-Popov operator can have zero modes even in the Abelian case. These zero modes cannot be eliminated by restricting the path integral over a certain region in the space of gauge potentials. The conditions for the existence of these zero modes are studied for static spherically symmetric spacetimes in arbitrary dimensions. For this class of metrics, the general analytic expression of the metric components in terms of the zero modes is constructed. Such expression allows one to find the asymptotic behavior of background metrics, which induce zero modes in the Coulomb gauge, an interesting example being the three-dimensional anti-de Sitter spacetime. Some of the implications for quantum field theory on curved spacetimes are discussed.

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)

Phase structure of lattice gauge theories for non-abelian subgroups of SU(3)

International Nuclear Information System (INIS)

Grosse, H.; Kuehnelt, H.

1981-01-01

The authors study the phase structure of Euclidean lattice gauge theories in four dimensions for certain non-abelian subgroups of SU(3) by using Monte-Carlo simulations and strong coupling expansions. As the order of the group increases a splitting of one phase transition into two is observed. (Auth.)

Gauge symmetries, topology, and quantisation

International Nuclear Information System (INIS)

Balachandran, A.P.

1994-01-01

The following two loosely connected sets of topics are reviewed in these lecture notes: (1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall effect. (2) Quantisation on multiply connected spaces and a topological proof the spin-statistics theorem which avoids quantum field theory and relativity. Under (1), after explaining the meaning of gauge invariance and the theory of constraints, we discuss boundary conditions on gauge transformations and the definition of internal symmetries in gauge field theories. We then show how the edge states in the quantum Hall effect can be derived from the Chern-Simons action using the preceding ideas. Under (2), after explaining the significance of fibre bundles for quantum physics, we review quantisation on multiply connected spaces in detail, explaining also mathematical ideas such as those of the universal covering space and the fundamental group. These ideas are then used to prove the aforementioned topological spin-statistics theorem

Invariant gauge families inherent in Abelian-gauge field theory. [Scalar dipole ghost field, free-field equations

Energy Technology Data Exchange (ETDEWEB)

Yokoyama, Kan-ichi; Kubo, Reijiro

1974-12-01

The framework of the Nakanishi-Lautrup formalism should be enlarged by introducing a scalar dipole ghost field B(x), which is called gauge on field, together with its pair field. By taking free Lagrangian density, Free-field equations can be described. The vacuum is defined by using a neutral vector field U..mu..(x). The state-vector space is generated by the adjoining conjugates of U..mu..sup((+))(x), and auxiliary fields B(x), B/sub 1/(x) and B/sub 2/(x), which were introduced in the form of the Lagrangian density. The physical states can be defined by the supplementary conditions of the form B/sub 1/sup((+))(x) 1 phys>=B/sub 2/sup((+))(x) 1 phys>=0. It is seen that all the field equations and all the commutators are kept form-invariant, and that the gauge parameter ..cap alpha.. is transformed into ..cap alpha..' given by ..cap alpha..'=..cap alpha..+lambda, with epsilon unchanged. The Lagrangian density is specified only by the gauge invariant parameter epsilon. The gauge structure of theory has universal meaning over whole Abelian-gauge field. C-number gauge transformation and the gauge structure in the presence of interaction are also discussed.

Bjorken-Johnson-Low technique and perturbation study on chiral anomaly in abelian coset pure gauge field theory

International Nuclear Information System (INIS)

Jing Sicong; Ruan Jie; AH. Dept. of Modern Physics)

1990-01-01

The perturbation theory in coset pure gauge field theory is studied for the first time. By using the Bjorken-johnson-Low technique and calculating the Schwinger term in related commutators, the anomalous Ward identity in Abelian coset pure gauge field theory is derived, which is consistent with the non-perutrbative calculation

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

Vortex-like and string-like solutions for the 2+1 dimensional SU(2) Yang-Mills theory with the Chern-Simons term

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

Linear supermultiplets and non-holomorphic gauge coupling functions

International Nuclear Information System (INIS)

Binetruy, P.; Grimm, R.; Girardi, G.

1991-04-01

The general couplings of linear multiplets, including Chern-Simons forms, to chiral matter as well as to the standard supergravity-matter system are constructed. Insisting on a canonically normalised Einstein term in particular the appearance of non-holomorphic gauge couplings are discussed and duality transformations in full generality are performed. The implications of these structures for the effective description of sigma model anomalies are presented with and without coupling to supergravity, following recent proposals of Derendinger, Ferrara, Kounnas and Zwirner and of Cardoso and Ovrut. (author) 14 refs

Theory and application of a gauge invariant effective action to the multi-loop renormalization of non-Abelian gauge theories

International Nuclear Information System (INIS)

Hart, C.F.

1981-01-01

A gauge invariant effective action which generalizes the usual background field method is applied to quantum non-Abelian gauge theories. The gauge properties of the theory as well as its equivalence to the conventional theory are presented. Solutions to the new effective field equations are found to be physical and it is shown how S-matrix elements may be computed in terms of this new effective action. Feynman rules are given and the renormalization theory is discussed using minimal subtraction and dimensional regularization. The resulting computation of counterterms is found to be simpler than that of the usual method. A complete two-loop calculation of the β function for pure Yang-Mills theory is given as a specific example of this approach

Soldering formalism in noncommutative field theory: a brief note

International Nuclear Information System (INIS)

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 orders in rigid states

International Nuclear Information System (INIS)

Wen, X.G.

1990-01-01

The authors study a new kind of ordering topological order in rigid states (the states with no local gapless excitations). This paper concentrates on characterization of the different topological orders. As an example the authors discuss in detail chiral spin states of 2+1 dimensional spin systems. Chiral spin states are described by the topological Chern-Simons theories in the continuum limit. The authors show that the topological orders can be characterized by a non-Abelian gauge structure over the moduli space which parametrizes a family of the model Hamiltonians supporting topologically ordered ground states. In 2 + 1 dimensions, the non-Abelian gauge structure determines possible fractional statistics of the quasi-particle excitations over the topologically ordered ground states. The dynamics of the low lying global excitations is shown to be independent of random spatial dependent perturbations. The ground state degeneracy and the non-Abelian gauge structures discussed in this paper are very robust, even against those perturbations that break translation symmetry. The authors also discuss the symmetry properties of the degenerate ground states of chiral spin states. The authors find that some degenerate ground states of chiral spin states on torus carry non-trivial quantum numbers of the 90 degrees rotation

Nilpotent symmetries and Curci-Ferrari-type restrictions in 2D non-Abelian gauge theory: Superfield approach

Science.gov (United States)

Srinivas, N.; Malik, R. P.

2017-11-01

We derive the off-shell nilpotent symmetries of the two (1 + 1)-dimensional (2D) non-Abelian 1-form gauge theory by using the theoretical techniques of the geometrical superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism. For this purpose, we exploit the augmented version of superfield approach (AVSA) and derive theoretically useful nilpotent (anti-)BRST, (anti-)co-BRST symmetries and Curci-Ferrari (CF)-type restrictions for the self-interacting 2D non-Abelian 1-form gauge theory (where there is no interaction with matter fields). The derivation of the (anti-)co-BRST symmetries and all possible CF-type restrictions are completely novel results within the framework of AVSA to BRST formalism where the ordinary 2D non-Abelian theory is generalized onto an appropriately chosen (2, 2)-dimensional supermanifold. The latter is parametrized by the superspace coordinates ZM = (xμ,𝜃,𝜃¯) where xμ (with μ = 0, 1) are the bosonic coordinates and a pair of Grassmannian variables (𝜃,𝜃¯) obey the relationships: 𝜃2 = 𝜃¯2 = 0, 𝜃𝜃¯ + 𝜃¯𝜃 = 0. The topological nature of our 2D theory allows the existence of a tower of CF-type restrictions.

Magnus forces and statistics in 2 + 1 dimensions

International Nuclear Information System (INIS)

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

Origin of Abelian Gauge Symmetries in Heterotic/F-theory Duality

CERN Document Server

Cvetic, Mirjam; Klevers, Denis; Poretschkin, Maximilian; Song, Peng

2016-01-01

We study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, we derive both the Calabi-Yau geometry as well as the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in their low energy effective theories: split spectral covers describing bundles with S(U(m) x U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m) x Z_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required ...

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.

Hidden singularities in non-abelian gauge fields

International Nuclear Information System (INIS)

Bollini, C.G.; Giambiagi, J.J.; Tiomno, J.

1978-01-01

It is shown that the potential (and field) of a non-abelian gauge theory is not well determined when it has a singular point. When this is the cause, it is important to specify the regularization procedure used to give a precise definition of physical quantities at the singularity at any stage of the computation. The fact that a certain A sub(μ) (associated with the given regularization) represents the vacuum when F sub(μν) is a zero distribution not only on the global space but also in all its projections to arbitrary subspaces is discussed. The example used as a base for the discussion is A vetor = i (sigma vetor Λ r vetor / r 2 ). For this example it is shown that different regularizations give the same field in the global space but they give different distributions when projected to subspaces containing the singular point [pt

Ponzano-Regge model revisited: I. Gauge fixing, observables and interacting spinning particles

International Nuclear Information System (INIS)

Freidel, Laurent; Louapre, David

2004-01-01

We show how to properly gauge fix all the symmetries of the Ponzano-Regge model for 3D quantum gravity. This amounts to doing explicit finite computations for transition amplitudes. We give the construction of the transition amplitudes in the presence of interacting quantum spinning particles. We introduce a notion of operators whose expectation value gives rise to either gauge fixing, introduction of time, or insertion of particles, according to the choice. We give the link between the spin foam quantization and the Hamiltonian quantization. We finally show the link between the Ponzano-Regge model and the quantization of Chern-Simons theory based on the double quantum group of SU(2)

Projected Entangled Pair States with non-Abelian gauge symmetries: An SU(2) study

Energy Technology Data Exchange (ETDEWEB)

Zohar, Erez, E-mail: erez.zohar@mpq.mpg.de [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching (Germany); Wahl, Thorsten B. [Rudolf Peierls Centre for Theoretical Physics, Oxford, 1 Keble Road, OX1 3NP (United Kingdom); Burrello, Michele, E-mail: michele.burrello@mpq.mpg.de [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching (Germany); Cirac, J. Ignacio [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching (Germany)

2016-11-15

Over the last years, Projected Entangled Pair States have demonstrated great power for the study of many body systems, as they naturally describe ground states of gapped many body Hamiltonians, and suggest a constructive way to encode and classify their symmetries. The PEPS study is not only limited to global symmetries, but has also been extended and applied for local symmetries, allowing to use them for the description of states in lattice gauge theories. In this paper we discuss PEPS with a local, SU(2) gauge symmetry, and demonstrate the use of PEPS features and techniques for the study of a simple family of many body states with a non-Abelian gauge symmetry. We present, in particular, the construction of fermionic PEPS able to describe both two-color fermionic matter and the degrees of freedom of an SU(2) gauge field with a suitable truncation.

Study of the maximal Abelian gauge in SU(2) Euclidean Yang-Mills theory in the presence of the Gribov horizon

International Nuclear Information System (INIS)

Capri, M. A. L.; Lemes, V. E. R.; Sobreiro, R. F.; Sorella, S. P.; Thibes, R.

2006-01-01

We pursue the study of SU(2) Euclidean Yang-Mills theory in the maximal Abelian gauge by taking into account the effects of the Gribov horizon. The Gribov approximation, previously introduced in [M. A. L. Capri, V. E. R. Lemes, R. F. Sobreiro, S. P. Sorella, and R. Thibes, Phys. Rev. D 72, 085021 (2005).], is improved through the introduction of the horizon function, which is constructed under the requirements of localizability and renormalizability. By following Zwanziger's treatment of the horizon function in the Landau gauge, we prove that, when cast in local form, the horizon term of the maximal Abelian gauge leads to a quantized theory which enjoys multiplicative renormalizability, a feature which is established to all orders by means of the algebraic renormalization. Furthermore, it turns out that the horizon term is compatible with the local residual U(1) Ward identity, typical of the maximal Abelian gauge, which is easily derived. As a consequence, the nonrenormalization theorem, Z g Z A 1/2 =1, relating the renormalization factors of the gauge coupling constant Z g and of the diagonal gluon field Z A , still holds in the presence of the Gribov horizon. Finally, we notice that a generalized dimension two gluon operator can be also introduced. It is BRST invariant on-shell, a property which ensures its multiplicative renormalizability. Its anomalous dimension is not an independent parameter of the theory, being obtained from the renormalization factors of the gauge coupling constant and of the diagonal antighost field

Field-strength formulation of gauge theories. The Hamiltonian approach in the Abelian theory

International Nuclear Information System (INIS)

Mendel, E.; Durand, L.

1984-01-01

We develop a Hamiltonian approach to the field-strength or dual formation of the Abelian gauge theory in which the potential A/sup μ/ is eliminated as a dynamical variable. Our work is based on the covariant gauge x/sup μ/A/sub μ/(x) = 0 which allows a simple elimination of A/sup μ/ in terms of the field strengths F/sup munu/. We obtain complete results for the generating functional for the Green's functions of the theory, Z = Z[f,g], where f and g are nonlocal currents coupled to E and B, and illustrate some unfamiliar aspects of the new formalism

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.

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.)

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

The Chern-Simons current in time series of knots and links in proteins

Science.gov (United States)

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.

Abelian dominance in Einstein’s theory

International Nuclear Information System (INIS)

Cho, Y M; Oh, S H; Kim, Sang-Woo

2012-01-01

We conjecture the Abelian dominance in Einstein’s theory, that is, the Abelian part of the theory plays the central role in the dynamics. Treating Einstein’s theory as a gauge theory of the Lorentz group, we show that Einstein’s theory can be decomposed into the restricted part made up of the restricted connection which has the full Lorentz gauge invariance and the valence part made up of the valence connection which plays the role of gravitational source of the restricted gravity. In this decomposition, the role of the metric g μν is replaced by a four-index metric tensor g μν which transforms covariantly under the Lorentz group, and the metric-compatibility condition ∇ α g μν = 0 of the connection is replaced by the gauge and generally covariant condition D μ g μν = 0. We show that there are two different Abelian decompositions, the light-like (or null) decomposition and the non-light-like (or non-null) decomposition, because the Lorentz group has two maximal Abelian subgroups. The decomposition shows the existence of the restricted gravity which has the full general invariance but is much simpler than Einstein’s theory. Moreover, it tells us that the restricted gravity can be written as an Abelian gauge theory, which implies that the graviton can be described by a massless spin-1 field. This establishes the Abelian dominance in Einstein’s theory. (paper)

The Topological Structure of the SU(2) Chern–Simons Topological Current in the Four-Dimensional Quantum Hall Effect

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)

Spin(7) instantons and the Hodge conjecture for certain abelian four-folds: A modest proposal

International Nuclear Information System (INIS)

Ramadas, T.R.

2008-04-01

The Hodge Conjecture is equivalent to a statement about conditions under which a complex vector bundle on a smooth complex projective variety (stably) admits a holomorphic structure. In the case of abelian four-folds, recent work in gauge theory suggests an approach using Spin(7) instantons. I advertise a class of examples due to Mumford where this approach could be tested. I construct explicit smooth vector bundles whose Chern characters are given Hodge classes - an instanton connection on these bundles would endow them with a holomorphic structure and thus prove that these classes are algebraic. I use complex multiplication to exhibit Cayley cycles representing the given Hodge classes. What is missing is an appropriate glueing theorem. (author)

Nonequilibrium formulation of abelian gauge theories

Energy Technology Data Exchange (ETDEWEB)

Zoeller, Thorsten

2013-09-01

This work is about a formulation of abelian gauge theories out-of-equilibrium. In contrast to thermal equilibrium, systems out-of-equilibrium are not constant in time, and the interesting questions in such systems refer to time evolution problems. After a short introduction to quantum electrodynamics (QED), the two-particle irreducible (2PI) effective action is introduced as an essential technique for the study of quantum field theories out-of-equilibrium. The equations of motion (EOMs) for the propagators of the theory are then derived from it. It follows a discussion of the physical degrees of freedom (DOFs) of the theory, in particular with respect to the photons, since in covariant formulations of gauge theories unphysical DOFs are necessarily contained. After that the EOMs for the photon propagator are examined more closely. It turns out that they are structurally complicated, and a reformulation of the equations is presented which for the untruncated theory leads to an essential structural simplification of the EOMs. After providing the initial conditions which are necessary in order to solve the EOMs, the free photon EOMs are solved with the help of the reformulated equations. It turns out that the solutions diverge in time, i.e. they are secular. This is a manifestation of the fact that gauge theories contain unphysical DOFs. It is reasoned that these secularities exist only in the free case and are therefore ''artificial''. It is however emphasized that they may not be a problem in principle, but certainly are in practice, in particular for the numerical solution of the EOMs. Further, the origin of the secularities, for which there exists an illustrative explanation, is discussed in more detail. Another characteristic feature of 2PI formulations of gauge theories is the fact that quantities calculated from approximations of the 2PI effective action, which are gauge invariant in the exact theory as well as in an approximated theory at

Gauge-invariant variational methods for Hamiltonian lattice gauge theories

International Nuclear Information System (INIS)

Horn, D.; Weinstein, M.

1982-01-01

This paper develops variational methods for calculating the ground-state and excited-state spectrum of Hamiltonian lattice gauge theories defined in the A 0 = 0 gauge. The scheme introduced in this paper has the advantage of allowing one to convert more familiar tools such as mean-field, Hartree-Fock, and real-space renormalization-group approximation, which are by their very nature gauge-noninvariant methods, into fully gauge-invariant techniques. We show that these methods apply in the same way to both Abelian and non-Abelian theories, and that they are at least powerful enough to describe correctly the physics of periodic quantum electrodynamics (PQED) in (2+1) and (3+1) space-time dimensions. This paper formulates the problem for both Abelian and non-Abelian theories and shows how to reduce the Rayleigh-Ritz problem to that of computing the partition function of a classical spin system. We discuss the evaluation of the effective spin problem which one derives the PQED and then discuss ways of carrying out the evaluation of the partition function for the system equivalent to a non-Abelian theory. The explicit form of the effective partition function for the non-Abelian theory is derived, but because the evaluation of this function is considerably more complicated than the one derived in the Abelian theory no explicit evaluation of this function is presented. However, by comparing the gauge-projected Hartree-Fock wave function for PQED with that of the pure SU(2) gauge theory, we are able to show that extremely interesting differences emerge between these theories even at this simple level. We close with a discussion of fermions and a discussion of how one can extend these ideas to allow the computation of the glueball and hadron spectrum

Hermitian (ϵ,δ)-Freudenthal-Kantor Triple Systems and Certain Applications of *-Generalized Jordan Triple Systems to Field Theory

International Nuclear Information System (INIS)

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

Statistical mechanics of an ideal gas of non-Abelian anyons

International Nuclear Information System (INIS)

Mancarella, Francesco; Trombettoni, Andrea; Mussardo, Giuseppe

2013-01-01

We study the thermodynamical properties of an ideal gas of non-Abelian Chern–Simons particles and we compute the second virial coefficient, considering the effect of general soft-core boundary conditions for the two-body wavefunction at zero distance. The behaviour of the second virial coefficient is studied as a function of the Chern–Simons coupling, the isospin quantum number and the hard-core parameters. Expressions for the main thermodynamical quantities at the lower order of the virial expansion are also obtained: we find that at this order the relation between the internal energy and the pressure is the same found (exactly) for 2D Bose and Fermi ideal gases. A discussion of the comparison of obtained findings with available results in literature for systems of hard-core non-Abelian Chern–Simons particles is also supplied.

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.)

Superfield approach to topological features of non-Abelian gauge theory

International Nuclear Information System (INIS)

Malik, R.P.

2002-01-01

We discuss some of the key topological aspects of a (1+1)-dimensional (2D) self-interacting non-Abelian gauge theory (having no interaction with matter fields) in the framework of chiral superfield formalism. We provide the geometrical interpretation for the Lagrangian density, symmetric energy-momentum tensor, topological invariants, etc, by exploiting the on-shell nilpotent BRST and co-BRST symmetries that emerge after the application of (dual) horizontality conditions. We show that the above physically interesting quantities geometrically correspond to the translation of some local (but composite) chiral superfields along one of the two independent Grassmannian directions of a (2+2)-dimensional supermanifold. This translation is generated by the conserved and on-shell nilpotent (co-)BRST charges that are present in the theory. (author)

Canonical quantization of non-abelian gauge theory in the Schroedinger picture: applications to monopoles and instantons

International Nuclear Information System (INIS)

Wadia, S.R.

1979-01-01

A detailed formulation of the quantum theory of non-abelian gauge fields is presented in the Schroedinger picture. It is applied to the semiclassical quantization of the t'Hoft-Polyakov monopole, with special attention paid to the treatment of boundary conditions and local and global gauge symmetry. The perturbation expansion is then discussed with the aid of standard collective co-ordinates. In the Prasad-Sommerfield limit, all the eigenfunctions of the fluctuation equation are presented, the ground-state wave function is constructed in terms of gauge and translation invariant co-ordinates, and its total angular momentum is computed to be zero. Aspects of instanton phenomena are then examined in the Schroedinger picture; the role of euclidean time is elucidated. The precise relation between boundary conditions, choice of gauge, and the corresponding picture of the semiclassical vacuum is demonstrated

Abelian versus non-abelian Higgs model in three dimensions

International Nuclear Information System (INIS)

Buchmueller, W.; Philipsen, O.

1995-04-01

We study the phase structure of the abelian Higgs model in three dimensions based on perturbation theory and a set of gauge independent gap equations for Higgs boson and vector boson masses. Contrary to the non-abelian Higgs model, the vector boson mass vanishes in the symmetric phase. In the Higgs phase the gap equations yield masses consistent with perturbation theory. The phase transition is first-order for small values of the scalar self-coupling λ, where the employed loop expansion is applicable. (orig.)

High-energy behaviour in a non-abelian gauge theory. Pt. 2

International Nuclear Information System (INIS)

Bartels, J.

1980-01-01

In this second part of our attempt to construct a unitary high-energy description of a spontaneously broken non-abelian gauge theory we calculate, for the n → m amplitude in the multi-Regge limit, the first corrections beyond the leading logarithmic approximation. The resulting amplitudes come in the form of the reggeon calculus where the number of reggeons in each t-channel is restricted to one or two. We then study the limit where the mass of the vector particle is taken to zero: for the 2 → 2 amplitude show that this limit exists, not only for the approximation of the present paper but also for higher-order corrections. (orig.)

The role of the anomaly cancellation mechanism in the evaluation of the radiatively induced Chern-Simons term in extended QED

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)

Localizing gauge fields on a topological Abelian string and the Coulomb law

International Nuclear Information System (INIS)

Torrealba S, Rafael S.

2010-01-01

The confinement of electromagnetic field is studied in axial symmetrical, warped, six-dimensional brane world, using a recently proposed topological Abelian string-vortex solution as background. It was found, that the massless gauge field fluctuations follow four-dimensional Maxwell equations in the Lorenz gauge. The massless zero mode is localized when the thickness of the string vortex is less than 5β/4πe 2 v 2 and there are no other localized massless modes. There is also an infinite of nonlocalized massive Fourier modes, that follow four-dimensional Proca equations with a continuous spectrum. To compute the corrections to the Coulomb potential, a radial cutoff was introduced, in order to achieve a discrete mass spectrum. As a main result, a (R o /βR 2 ) correction was found for the four-dimensional effective Coulomb law; the result is in correspondence with the observed behavior of the Coulomb potential at today's measurable distances.

Mean field theory for non-abelian gauge theories and fluid dynamics. A brief progress report

International Nuclear Information System (INIS)

Wadia, Spenta R.

2009-01-01

We review the long standing problem of 'mean field theory' for non-abelian gauge theories. As a consequence of the AdS/CFT correspondence, in the large N limit, at strong coupling, and high temperatures and density, the 'mean field theory' is described by the Navier-Stokes equations of fluid dynamics. We also discuss and present results on the non-conformal fluid dynamics of the D1 brane in 1+1 dim. (author)

SU(N) chiral gauge theories on the lattice

International Nuclear Information System (INIS)

Golterman, Maarten; Shamir, Yigal

2004-01-01

We extend the construction of lattice chiral gauge theories based on non-perturbative gauge fixing to the non-Abelian case. A key ingredient is that fermion doublers can be avoided at a novel type of critical point which is only accessible through gauge fixing, as we have shown before in the Abelian case. The new ingredient allowing us to deal with the non-Abelian case as well is the use of equivariant gauge fixing, which handles Gribov copies correctly, and avoids Neuberger's no-go theorem. We use this method in order to gauge fix the non-Abelian group (which we will take to be SU(N)) down to its maximal Abelian subgroup. Obtaining an undoubled, chiral fermion content requires us to gauge-fix also the remaining Abelian gauge symmetry. This modifies the equivariant Becchi-Rouet-Stora-Tyutin (BRST) identities, but their use in proving unitarity remains intact, as we show in perturbation theory. On the lattice, equivariant BRST symmetry as well as the Abelian gauge invariance are broken, and a judiciously chosen irrelevant term must be added to the lattice gauge-fixing action in order to have access to the desired critical point in the phase diagram. We argue that gauge invariance is restored in the continuum limit by adjusting a finite number of counter terms. We emphasize that weak-coupling perturbation theory applies at the critical point which defines the continuum limit of our lattice chiral gauge theory

Gravity/Fluid Correspondence and Its Application on Bulk Gravity with U(1) Gauge Field

International Nuclear Information System (INIS)

Hu, Ya-Peng; Zhang, Jian-Hui

2014-01-01

As the long wavelength limit of the AdS/CFT correspondence, the gravity/fluid correspondence has been shown to be a useful tool for extracting properties of the fluid on the boundary dual to the gravity in the bulk. In this paper, after briefly reviewing the algorithm of gravity/fluid correspondence, we discuss the results of its application on bulk gravity with a U(1) gauge field. In the presence of a U(1) gauge field, the dual fluid possesses more interesting properties such as its charge current. Furthermore, an external field A_μ"e"x"t could affect the charge current, and the U(1) Chern-Simons term also induces extra structures to the dual current giving anomalous transport coefficients.

Generalized ward identities for non-local transformation

International Nuclear Information System (INIS)

Li Ziping; Li Ruijie

2002-01-01

Based on the phase-space generating functional of Green function for a system with a singular higher-order Lagrangian, the generalized canonical Ward identities under the local and non-local transformation in phase space for such a system have been derived. Starting from the configuration-space generating functional for a gauge-invariant system, the generalized Ward identities were deduced under the local, non-local and global transformation, respectively. The applications to the non-Abelian Chern-Simons theories with higher derivatives were given. Some relationships among the proper vertices have been deduced, in which one does not need to carry out the integration over canonical momenta in phase-space generating functional. The Ward-Takahashi identities for BRS transformation are also obtained

Perturbative search for dead-end CFTs

International Nuclear Information System (INIS)

Nakayama, Yu

2015-01-01

To explore the possibility of self-organized criticality, we look for CFTs without any relevant scalar deformations (a.k.a. dead-end CFTs) within power-counting renormalizable quantum field theories with a weakly coupled Lagrangian description. In three dimensions, the only candidates are pure (Abelian) gauge theories, which may be further deformed by Chern-Simons terms. In four dimensions, we show that there are infinitely many non-trivial candidates based on chiral gauge theories. Using the three-loop beta functions, we compute the gap of scaling dimensions above the marginal value, and it can be as small as O(10"−"5) and robust against the perturbative corrections. These classes of candidates are very weakly coupled and our perturbative conclusion seems difficult to refute. Thus, the hypothesis that non-trivial dead-end CFTs do not exist is likely to be false in four dimensions.

On the gauge orbit space stratification: a review

International Nuclear Information System (INIS)

Rudolph, G.; Schmidt, M.; Volobuev, I.P.

2002-01-01

First, we review the basic mathematical structures and results concerning the gauge orbit space stratification. This includes general properties of the gauge group action, fibre bundle structures induced by this action, basic properties of the stratification and the natural Riemannian structures of the strata. In the second part, we study the stratification for theories with gauge group SU(n) in spacetime dimension 4. We develop a general method for determining the orbit types and their partial ordering, based on the 1-1 correspondence between orbit types and holonomy-induced Howe subbundles of the underlying principal SU(n)-bundle. We show that the orbit types are classified by certain cohomology elements of spacetime satisfying two relations and that the partial ordering is characterized by a system of algebraic equations. Moreover, operations for generating direct successors and direct predecessors are formulated, which allow one to construct the set of orbit types, starting from the principal type. Finally, we discuss an application to nodal configurations in Yang-Mills-Chern-Simons theory. (author)

Abelian projection at the multi-instanton

International Nuclear Information System (INIS)

Fukushima, M.

2001-01-01

We study full non-Abelian, Abelian projected lattice field configurations built up from random instanton gas configurations in the continuum. We study the instanton contribution to the Q-barQ force with respect to whether various versions of Abelian dominance hold. We show that the lattice used to discretize the instanton gas configurations has to be sufficiently coarse (a ≅ 2ρ-bar compared with the instanton size ρ-bar) such that maximal Abelian gauge projection as well as the monopole gas contribution to the Q-barQ force reproduce the non-Abelian instanton-mediated force in the intermediate range of linear quasi-confinement. (author)

Plasma instabilities and turbulence in non-Abelian gauge theories

Energy Technology Data Exchange (ETDEWEB)

Scheffler, Sebastian Herwig Juergen

2010-02-17

Several aspects of the thermalisation process in non-Abelian gauge theories are investigated. Both numerical simulations in the classical statistical approximation and analytical computations in the framework of the two-particle-irreducible effective action are carried out and their results are compared to each other. The physical quantities of central importance are the correlation functions of the gauge field in Coulomb and temporal axial gauge as well as the gauge invariant energy-momentum tensor. Following a general introduction, the theoretical framework of the ensuing investigations is outlined. In doing so, the range of validity of the employed approximation schemes is discussed as well. The first main part of the thesis is concerned with the early stage of the thermalisation process where particular emphasis is on the role of plasma instabilities. These investigations are relevant to the phenomenological understanding of present heavy ion collision experiments. First, an ensemble of initial conditions motivated by the ''colour glass condensate'' is developed which captures characteristic properties of the plasma created in heavy ion collisions. Here, the strong anisotropy and the large occupation numbers of low-momentum degrees of freedom are to be highlighted. Numerical calculations demonstrate the occurrence of two kinds of instabilities. Primary instabilities result from the specific initial conditions. Secondary instabilities are caused by nonlinear fluctuation effects of the preceding primary instabilities. The time scale associated with the instabilities is of order 1 fm/c. It is shown that the plasma instabilities isotropize the initially strongly anisotropic ensemble in the domain of low momenta (gauge group SU(2) to SU(3) by a simple rescaling procedure. Finally, the role of Nielsen-Olesen instabilities in an idealised setup is investigated. In the second part, the

Plasma instabilities and turbulence in non-Abelian gauge theories

International Nuclear Information System (INIS)

Scheffler, Sebastian Herwig Juergen

2010-01-01

Several aspects of the thermalisation process in non-Abelian gauge theories are investigated. Both numerical simulations in the classical statistical approximation and analytical computations in the framework of the two-particle-irreducible effective action are carried out and their results are compared to each other. The physical quantities of central importance are the correlation functions of the gauge field in Coulomb and temporal axial gauge as well as the gauge invariant energy-momentum tensor. Following a general introduction, the theoretical framework of the ensuing investigations is outlined. In doing so, the range of validity of the employed approximation schemes is discussed as well. The first main part of the thesis is concerned with the early stage of the thermalisation process where particular emphasis is on the role of plasma instabilities. These investigations are relevant to the phenomenological understanding of present heavy ion collision experiments. First, an ensemble of initial conditions motivated by the ''colour glass condensate'' is developed which captures characteristic properties of the plasma created in heavy ion collisions. Here, the strong anisotropy and the large occupation numbers of low-momentum degrees of freedom are to be highlighted. Numerical calculations demonstrate the occurrence of two kinds of instabilities. Primary instabilities result from the specific initial conditions. Secondary instabilities are caused by nonlinear fluctuation effects of the preceding primary instabilities. The time scale associated with the instabilities is of order 1 fm/c. It is shown that the plasma instabilities isotropize the initially strongly anisotropic ensemble in the domain of low momenta (< or similar 1 GeV). Essential results can be translated from the gauge group SU(2) to SU(3) by a simple rescaling procedure. Finally, the role of Nielsen-Olesen instabilities in an idealised setup is investigated. In the second part, the quasi

Properties of Gribov region and horizon function in the SU(N) Maximal Abelian Gauge

International Nuclear Information System (INIS)

Capri, Marcio Andre Lopes; Gomez, A.J.; Guimaraes, M.S.; Lemes, Vitor Emanuel Rodino; Sorella, Silvio Paolo

2011-01-01

Full text: The problem of the Gribov copies deals with the impossibility of to choose a unique gauge condition in the quantization process in the Yang Mills theories. In the Landau gauge, several properties of the Gribov region are established, the implementation of the Gribov copies in the path integral is taking account by the introduction of the horizon function directly in the action giving rise to modifications in the ghost and gluon propagator in the infrared regime. However, is interesting to looking at other gauge choices for obtain additional information of the phenomena, and compare our results in the landau gauge. In this work we address the issue of the Gribov copies in SU(N),N ¿ 2, Euclidean Yang-Mills theories quantized in the maximal Abelian gauge. A few properties of the Gribov region in this gauge are established. Similarly to the case of SU(2), the Gribov region turns out to be convex, bounded along the off-diagonals directions in field space, and unbounded along the diagonal ones. The implementation of the restriction to the Gribov region in the functional integral is discussed through the introduction of the horizon function, whose construction will be outlined in detail. The influence of this restriction on the behavior of the gluon and ghost propagators of the theory is also investigated together with a set of dimension two condensates. (author)

Restricted gravity: Abelian projection of Einstein's theory

International Nuclear Information System (INIS)

Cho, Y.M.

2013-01-01

Treating Einstein's theory as a gauge theory of Lorentz group, we decompose the gravitational connection Γμ into the restricted connection made of the potential of the maximal Abelian subgroup H of Lorentz group G and the valence connection made of G/H part of the potential which transforms covariantly under Lorentz gauge transformation. With this we show that Einstein's theory can be decomposed into the restricted gravity made of the restricted connection which has the full Lorentz gauge invariance which has the valence connection as gravitational source. The decomposition shows the existence of a restricted theory of gravitation which has the full general invariance but is much simpler than Einstein's theory. Moreover, it tells that the restricted gravity can be written as an Abelian gauge theory,

Nonperturbative dynamics of hot non-Abelian gauge fields: Beyond the leading log approximation

International Nuclear Information System (INIS)

Arnold, Peter; Yaffe, Laurence G.

2000-01-01

Many aspects of high-temperature gauge theories, such as the electroweak baryon number violation rate, color conductivity, and the hard gluon damping rate, have previously been understood only at leading logarithmic order (that is, neglecting effects suppressed only by an inverse logarithm of the gauge coupling). We discuss how to systematically go beyond leading logarithmic order in the analysis of physical quantities. Specifically, we extend to next-to-leading-log order (NLLO) the simple leading-log effective theory due to Bo''deker that describes non-perturbative color physics in hot non-Abelian plasmas. A suitable scaling analysis is used to show that no new operators enter the effective theory at next-to-leading-log order. However, a NLLO calculation of the color conductivity is required, and we report the resulting value. Our NLLO result for the color conductivity can be trivially combined with previous numerical work by Moore to yield a NLLO result for the hot electroweak baryon number violation rate

Relativistic generalization and extension to the non-Abelian gauge theory of Feynman's proof of the Maxwell equations

International Nuclear Information System (INIS)

Tanimura, Shogo

1992-01-01

R. P. Feynman showed F. J. Dyson a proof of the Lorentz force law and the homogeneous Maxwell equations, which he obtained starting from Newton's law of motion and the commutation relations between position and velocity for a single nonrelativistic particle. The author formulate both a special relativistic and a general relativistic version of Feynman's derivation. Especially in the general relativistic version they prove that the only possible fields that can consistently act on a quantum mechanical particle are scalar, gauge, and gravitational fields. They also extend Feynman's scheme to the case of non-Abelian gauge theory in the special relativistic context. 8 refs

A 3d-3d appetizer

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.

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

3D gauged supergravity from SU(2) reduction of $N=1$ 6D supergravity

CERN Document Server

Gava, Edi; Narain, K S

2010-01-01

We obtain Yang-Mills $SU(2)\\times G$ gauged supergravity in three dimensions from $SU(2)$ group manifold reduction of (1,0) six dimensional supergravity coupled to an anti-symmetric tensor multiplet and gauge vector multiplets in the adjoint of $G$. The reduced theory is consistently truncated to $N=4$ 3D supergravity coupled to $4(1+\\textrm{dim}\\, G)$ bosonic and $4(1+\\textrm{dim}\\, G)$ fermionic propagating degrees of freedom. This is in contrast to the reduction in which there are also massive vector fields. The scalar manifold is $\\mathbf{R}\\times \\frac{SO(3,\\, \\textrm{dim}\\, G)}{SO(3)\\times SO(\\textrm{dim}\\, G)}$, and there is a $SU(2)\\times G$ gauge group. We then construct $N=4$ Chern-Simons $(SO(3)\\ltimes \\mathbf{R}^3)\\times (G\\ltimes \\mathbf{R}^{\\textrm{dim}G})$ three dimensional gauged supergravity with scalar manifold $\\frac{SO(4,\\,1+\\textrm{dim}G)}{SO(4)\\times SO(1+\\textrm{dim}G)}$ and explicitly show that this theory is on-shell equivalent to the Yang-Mills $SO(3)\\times G$ gauged supergravity the...

Exact diagonalization of cubic lattice models in commensurate Abelian magnetic fluxes and translational invariant non-Abelian potentials

DEFF Research Database (Denmark)

Burrello, M.; Fulga, Ion Cosma; Lepori, L.

2017-01-01

of a translational invariant non-Abelian coupling for multi-component spinors does not affect the dimension of the minimal Hamiltonian blocks, nor the dimension of the magnetic Brillouin zone. General formulas are presented for the U(2) case and explicit examples are investigated involving π and 2π/3 magnetic fluxes......We present a general analytical formalism to determine the energy spectrum of a quantum particle in a cubic lattice subject to translationally invariant commensurate magnetic fluxes and in the presence of a general spaceindependent non-Abelian gauge potential. We first review and analyze the case...... of purely Abelian potentials, showing also that the so-called Hasegawa gauge yields a decomposition of the Hamiltonian into sub-matrices having minimal dimension. Explicit expressions for such matrices are derived, also for general anisotropic fluxes. Later on, we show that the introduction...

Two-loop ghost-antighost condensation for SU(2) Yang-Mills theories in the maximal abelian gauge

International Nuclear Information System (INIS)

Fazio, A.R.

2004-01-01

In the framework of the formalism of Cornwall et.al. for composite operators I study the ghost-antighost condensation in SU(2) Yang-Mills theories quantized in the Maximal Abelian Gauge and derive analytically a condensating effective potential at two ghost loops. I find that in this approximation the one-loop pairing ghost-antighost is not destroyed and no mass is generated if the ansatz for the propagator suggested by the tree level Hubbard-Stratonovich transformations is used

Noncommutative gauge theory for Poisson manifolds

Energy Technology Data Exchange (ETDEWEB)

Jurco, Branislav E-mail: jurco@mpim-bonn.mpg.de; Schupp, Peter E-mail: schupp@theorie.physik.uni-muenchen.de; Wess, Julius E-mail: wess@theorie.physik.uni-muenchen.de

2000-09-25

A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem.

Noncommutative gauge theory for Poisson manifolds

International Nuclear Information System (INIS)

Jurco, Branislav; Schupp, Peter; Wess, Julius

2000-01-01

A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem

Gauge/gravity duality applied to condensed matter systems

International Nuclear Information System (INIS)

Ammon, Martin Matthias

2010-01-01

DE024486693In the present thesis by means of the AdS/CFT correspondence phenomena of strongly coupled quantum critical systems are studied. Hereby the assumption developed 1997 by Maldacena puts four-dimensional N=4 supersymmetric Yang-Mills theory and type IIB supergravity in the five-dimensional anti-de Sitter space in relation. This assumption can be generalized in different ways. So on the gauge-theory side states with finite temperature and density can be considered or degrees of freedom added, which transform in the fundamental representation of the gauge group, the so-called flavor degrees of freedom. These deformations of the correspondence are applied in the present thesis in order to understand better strongly coupled systems in the neighbourhood of quantum-critical points. We approximate hereby the field theory at the quantum-critical point by N=4 supersymmetric Yang-Mills theory. The charge carriers of the system are introduced by supersymmetric flavor fields. For instance in the present thesis in the case of two flavor fields, which have the same mass, a chemical potential for the isospin is considered and the phase diagram studied. The isospin-chemical potential breaks hereby the non-Abelian part of the flavor symmetry SU(2) to U(1). If a critical value of the isospin-chemical potential is exceeded, so shows our calculation, that the strongly coupled system becomes unstable against fluctuations. A new thermodynamically favorized state is formed. This state breaks the residual U(1) flavor symmetry spontaneously and can therefore be considered as a superfluid. If U(1) is gauged, by this way a superconductor is obtained. The AC conductivity goes in the superconducting phase for small frequencies to zero. The DC conductivity however is infinite. Furthermore we calculate the Fermi surface in the superconducting phase. Furthermore a holographic method for the calculation of the DC conductivity in arbitrarily constant electric and magnetic fields is further

Gauge/gravity duality applied to condensed matter systems

Energy Technology Data Exchange (ETDEWEB)

Ammon, Martin Matthias

2010-07-07

DE024486693In the present thesis by means of the AdS/CFT correspondence phenomena of strongly coupled quantum critical systems are studied. Hereby the assumption developed 1997 by Maldacena puts four-dimensional N=4 supersymmetric Yang-Mills theory and type IIB supergravity in the five-dimensional anti-de Sitter space in relation. This assumption can be generalized in different ways. So on the gauge-theory side states with finite temperature and density can be considered or degrees of freedom added, which transform in the fundamental representation of the gauge group, the so-called flavor degrees of freedom. These deformations of the correspondence are applied in the present thesis in order to understand better strongly coupled systems in the neighbourhood of quantum-critical points. We approximate hereby the field theory at the quantum-critical point by N=4 supersymmetric Yang-Mills theory. The charge carriers of the system are introduced by supersymmetric flavor fields. For instance in the present thesis in the case of two flavor fields, which have the same mass, a chemical potential for the isospin is considered and the phase diagram studied. The isospin-chemical potential breaks hereby the non-Abelian part of the flavor symmetry SU(2) to U(1). If a critical value of the isospin-chemical potential is exceeded, so shows our calculation, that the strongly coupled system becomes unstable against fluctuations. A new thermodynamically favorized state is formed. This state breaks the residual U(1) flavor symmetry spontaneously and can therefore be considered as a superfluid. If U(1) is gauged, by this way a superconductor is obtained. The AC conductivity goes in the superconducting phase for small frequencies to zero. The DC conductivity however is infinite. Furthermore we calculate the Fermi surface in the superconducting phase. Furthermore a holographic method for the calculation of the DC conductivity in arbitrarily constant electric and magnetic fields is further

V A Fock and gauge symmetry

International Nuclear Information System (INIS)

Okun, Lev B

2010-01-01

V A Fock, in 1926, was the first to have the idea of an Abelian gradient transformation and to discover that the electromagnetic interaction of charged particles has a gradient invariance in the framework of quantum mechanics. These transformation and invariance were respectively named Eichtransformation and Eichinvarianz by H Weyl in 1929 (the German verb zu eichen means to gauge). The first non-Abelian gauge theory was suggested by O Klein in 1938; and in 1954, C N Yang and R L Mills rediscovered the non-Abelian gauge symmetry. Gauge invariance is the underlying principle of the current Standard Model of strong and electroweak interactions. (from the history of physics)

Vortex structure in abelian-projected lattice gauge theory

International Nuclear Information System (INIS)

Ambjoern, J.; Giedt, J.; Greensite, J.

2000-01-01

We report on a breakdown of both monopole dominance and positivity in abelian-projected lattice Yang-Mills theory. The breakdown is associated with observables involving two units of the abelian charge. We find that the projected lattice has at most a global Z 2 symmetry in the confined phase, rather than the global U(1) symmetry that might be expected in a dual superconductor or monopole Coulomb gas picture. Implications for monopole and center vortex theories of confinement are discussed

Abelian gauge theories with tensor gauge fields

International Nuclear Information System (INIS)

Kapuscik, E.

1984-01-01

Gauge fields of arbitrary tensor type are introduced. In curved space-time the gravitational field serves as a bridge joining different gauge fields. The theory of second order tensor gauge field is developed on the basis of close analogy to Maxwell electrodynamics. The notion of tensor current is introduced and an experimental test of its detection is proposed. The main result consists in a coupled set of field equations representing a generalization of Maxwell theory in which the Einstein equivalence principle is not satisfied. (author)

Origin of Abelian gauge symmetries in heterotic/F-theory duality

International Nuclear Information System (INIS)

Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis; Poretschkin, Maximilian; Song, Peng

2016-01-01

We study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, we derive both the Calabi-Yau geometry as well as the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in their low energy effective theories: split spectral covers describing bundles with S(U(m)×U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m)×ℤ_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required that the elliptic fibration on the heterotic side has a non-trivial Mordell-Weil group. While the number of geometrically massless U(1)’s is determined entirely by geometry on the F-theory side, on the heterotic side the correct number of U(1)’s is found by taking into account a Stückelberg mechanism in the lower-dimensional effective theory. In geometry, this corresponds to the condition that sections in the two half K3 surfaces that arise in the stable degeneration limit of F-theory can be glued together globally.

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.

Critical properties of effective gauge theories for novel quantum fluids

Energy Technology Data Exchange (ETDEWEB)

Smoergrav, Eivind

2005-07-01

Critical properties of U(1) symmetric gauge theories are studied in 2+1 dimensions, analytically through duality transformations and numerically through Monte Carlo simulations. Physical applications range from quantum phase transitions in two dimensional insulating materials to superfluid and superconducting properties of light atoms such as hydrogen under extreme pressure. A novel finite size scaling method, utilizing the third moment M{sub 3} of the action, is developed. Finite size scaling analysis of M{sub 3} yields the ratio (1 + alpha)/ny and 1/ny separately, so that critical exponents alpha and ny can be obtained independently without invoking hyperscaling. This thesis contains eight research papers and an introductory part covering some basic concepts and techniques. Paper 1: The novel M{sub 3} method is introduced and employed together with Monte Carlo simulations to study the compact Abelian Higgs model in the adjoint representation with q = 2. Paper 2: We study phase transitions in the compact Abelian Higgs model for fundamental charge q = 2; 3; 4; 5. Various other models are studied to benchmark the M{sub 3} method. Paper 3: This is a proceeding paper based on a talk given by F. S. Nogueira at the Aachen EPS HEP 2003 conference. A review of the results from Paper 1 and Paper 2 on the compact Abelian Higgs model together with some results on q = 1 obtained by F. S. Nogueira, H. Kleinert, and A. Sudboe is given. Paper 4: The effect of a Chern-Simons (CS) term in the phase structure of two Abelian gauge theories is studied. Paper 5: We study the critical properties of the N-component Ginzburg-Landau theory. Paper 6: We consider the vortices in the 2-component Ginzburg-Landau model in a finite but low magnetic field. The ground state is a lattice of co centered vortices in both order parameters. We find two novel phase transitions. i) A 'vortex sub-lattice melting' transition where vortices in the field with lowest phase stiffness (&apos

Local gauge coupling running in supersymmetric gauge theories on orbifolds

International Nuclear Information System (INIS)

Hillenbach, M.

2007-01-01

By extending Feynman's path integral calculus to fields which respect orbifold boundary conditions we provide a straightforward and convenient framework for loop calculations on orbifolds. We take advantage of this general method to investigate supersymmetric Abelian and non-Abelian gauge theories in five, six and ten dimensions where the extra dimensions are compactified on an orbifold. We consider hyper and gauge multiplets in the bulk and calculate the renormalization of the gauge kinetic term which in particular allows us to determine the gauge coupling running. The renormalization of the higher dimensional theories in orbifold spacetimes exhibits a rich structure with three principal effects: Besides the ordinary renormalization of the bulk gauge kinetic term the loop effects may require the introduction of both localized gauge kinetic terms at the fixed points/planes of the orbifold and higher dimensional operators. (orig.)

Local gauge coupling running in supersymmetric gauge theories on orbifolds

Energy Technology Data Exchange (ETDEWEB)

Hillenbach, M.

2007-11-21

By extending Feynman's path integral calculus to fields which respect orbifold boundary conditions we provide a straightforward and convenient framework for loop calculations on orbifolds. We take advantage of this general method to investigate supersymmetric Abelian and non-Abelian gauge theories in five, six and ten dimensions where the extra dimensions are compactified on an orbifold. We consider hyper and gauge multiplets in the bulk and calculate the renormalization of the gauge kinetic term which in particular allows us to determine the gauge coupling running. The renormalization of the higher dimensional theories in orbifold spacetimes exhibits a rich structure with three principal effects: Besides the ordinary renormalization of the bulk gauge kinetic term the loop effects may require the introduction of both localized gauge kinetic terms at the fixed points/planes of the orbifold and higher dimensional operators. (orig.)

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

Faddeev–Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions

Energy Technology Data Exchange (ETDEWEB)

Escalante, Alberto, E-mail: aescalan@ifuap.buap.mx; Manuel-Cabrera, J., E-mail: jmanuel@ifuap.buap.mx

2015-10-15

A detailed Faddeev–Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions is performed. We obtain for the theories under study the constraints, the gauge transformations, the generalized Faddeev–Jackiw brackets and we perform the counting of physical degrees of freedom. In addition, we compare our results with those found in the literature where the canonical analysis is developed, in particular, we show that both the generalized Faddeev–Jackiw brackets and Dirac’s brackets coincide to each other. Finally we discuss some remarks and prospects. - Highlights: • A detailed Faddeev–Jackiw analysis for exotic action of gravity is performed. • We show that Dirac’s brackets and Generalized [FJ] brackets are equivalent. • Without fixing the gauge exotic action is a non-commutative theory. • The fundamental gauge transformations of the theory are found. • Dirac and Faddeev–Jackiw approaches are compared.

Abelian gauge potentials on cubic lattices

DEFF Research Database (Denmark)

Burrello, M.; Lepori, L.; Paganelli, S.

2017-01-01

The study of the properties of quantum particles in a periodic potential subjected to a magnetic field is an active area of research both in physics and mathematics, and it has been and is yet deeply investigated. In this chapter we discuss how to implement and describe tunable Abelian magnetic...... potentials in one-dimensional rings....

A non-perturbative argument for the non-abelian Higgs mechanism

International Nuclear Information System (INIS)

De Palma, G.; Strocchi, F.

2013-01-01

The evasion of massless Goldstone bosons by the non-abelian Higgs mechanism is proved by a non-perturbative argument in the local BRST gauge. -- Highlights: •The perturbative explanation of the Higgs mechanism (HM) is not under mathematical control. •We offer a non-perturbative proof of the absence of Goldstone bosons from the non-abelian HM. •Our non-perturbative proof in the BRST gauge avoids a mean field ansatz and expansion

A non-perturbative argument for the non-abelian Higgs mechanism

Energy Technology Data Exchange (ETDEWEB)

De Palma, G. [Scuola Normale Superiore, Pisa (Italy); INFN, Sezione di Pisa, Pisa (Italy); Strocchi, F., E-mail: franco.strocchi@sns.it [INFN, Sezione di Pisa, Pisa (Italy)

2013-09-15

The evasion of massless Goldstone bosons by the non-abelian Higgs mechanism is proved by a non-perturbative argument in the local BRST gauge. -- Highlights: •The perturbative explanation of the Higgs mechanism (HM) is not under mathematical control. •We offer a non-perturbative proof of the absence of Goldstone bosons from the non-abelian HM. •Our non-perturbative proof in the BRST gauge avoids a mean field ansatz and expansion.

Equivariant Verlinde Formula from Fivebranes and Vortices

Science.gov (United States)

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.

Classical solutions in lattice gauge theories

International Nuclear Information System (INIS)

Mitrjushkin, V.K.

1996-08-01

The solutions of the classical equations of motion on a periodic lattice are found which correspond to abelian single and double Dirac sheets. These solutions exist also in non-abelian theories. Possible applications of these solutions to the calculation of gauge dependent and gauge invariant observables are discussed. (orig.)

Bootstrapping non-commutative gauge theories from L∞ algebras

Science.gov (United States)

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.

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

Gauge invariance and anomalous theories at finite fermionic density

International Nuclear Information System (INIS)

Roberge, A.

1990-01-01

We investigate the issue of stability of anomalous matter at finite fermionic density using a two-dimensional toy model. In particular, we pay careful attention to the issue of gauge invariance. We find that, contrary to some recent claims, the effective free energy (obtained by integrating out the fermions) cannot be obtained by the simple inclusion of a Chern-Simons term multiplying the fermionic chemical potential. We obtain some conditions for stability of anomalous charges when some finite density of conserved charge is present as well as for the neutral case. We also show that, under reasonable conditions, no sphaleron-type solution can exist in the toy model unless the anomalous charge density vanishes. We argue that this could be the case for more realistic models as well

Phase structure and critical properties of an abelian gauge theory

Energy Technology Data Exchange (ETDEWEB)

Mo, Sjur

2001-12-01

The main new results are presented in the form of three papers at the end of this thesis. The main topic is Monte-Carlo studies of the phase structure and critical properties of the phenomenological Ginzburg-Landau model, i.e. an abelian gauge theory. However, the first paper is totally different and deals with microscopic theory for lattice-fermions in a magnetic field. Paper I is about ''Fermion-pairing on a square lattice in extreme magnetic fields''. We consider the Cooper-problem on a two-dimensional, square lattice with a uniform, perpendicular magnetic field. Only rational flux fractions are considered. An extended (real-space) Hubbard model including nearest and next nearest neighbor interactions is transformed to ''k-space'', or more precisely, to the space of eigenfunctions of Harper's equation, which constitute basis functions of the magnetic translation group for the lattice. A BCS-like truncation of the interaction term is performed. Expanding the interactions in the basis functions of the irreducible representations of the point group C{sub 4{nu}} of the square lattice simplify calculations. The numerical results indicate enhanced binding compared to zero magnetic field, and thus re-entrant superconducting pairing at extreme magnetic fields, well beyond the point where the usual semi-classical treatment of the magnetic field breaks down. Paper II is about the ''Hausdorff dimension of critical fluctuations in abelian gauge theories''. Here we analyze the geometric properties of the line-like critical fluctuations (vortex loops) in the Ginzburg-Landau model in zero magnetic background field. By using a dual description, we obtain scaling relations between exponents of geometric arid thermodynamic nature. In particular we connect the anomalous scaling dimension {eta} of the dual matter field to the Hausdorff or fractal dimension D{sub H} of the critical fluctuations, in the original model

Non-Abelian string and particle braiding in topological order: Modular SL (3 ,Z ) representation and (3 +1 ) -dimensional twisted gauge theory

Science.gov (United States)

Wang, Juven C.; Wen, Xiao-Gang

2015-01-01

String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group G and a 4-cocycle twist ω4 of G 's cohomology group H4(G ,R /Z ) in three-dimensional space and one-dimensional time (3 +1 D ) . We establish the topological spin and the spin-statistics relation for the closed strings and their multistring braiding statistics. The 3 +1 D twisted gauge theory can be characterized by a representation of a modular transformation group, SL (3 ,Z ) . We express the SL (3 ,Z ) generators Sx y z and Tx y in terms of the gauge group G and the 4-cocycle ω4. As we compactify one of the spatial directions z into a compact circle with a gauge flux b inserted, we can use the generators Sx y and Tx y of an SL (2 ,Z ) subgroup to study the dimensional reduction of the 3D topological order C3 D to a direct sum of degenerate states of 2D topological orders Cb2 D in different flux b sectors: C3 D=⊕bCb2 D . The 2D topological orders Cb2 D are described by 2D gauge theories of the group G twisted by the 3-cocycle ω3 (b ), dimensionally reduced from the 4-cocycle ω4. We show that the SL (2 ,Z ) generators, Sx y and Tx y, fully encode a particular type of three-string braiding statistics with a pattern that is the connected sum of two Hopf links. With certain 4-cocycle twists, we discover that, by threading a third string through two-string unlink into a three-string Hopf-link configuration, Abelian two-string braiding statistics is promoted to non-Abelian three-string braiding statistics.

New scheme for color confinement and violation of the non-Abelian Bianchi identities

Science.gov (United States)

Suzuki, Tsuneo; Ishiguro, Katsuya; Bornyakov, Vitaly

2018-02-01

A new scheme for color confinement in QCD due to violation of the non-Abelian Bianchi identities is proposed. The violation of the non-Abelian Bianchi identities (VNABI) Jμ is equal to Abelian-like monopole currents kμ defined by the violation of the Abelian-like Bianchi identities. Although VNABI is an adjoint operator satisfying the covariant conservation law DμJμ=0 , it satisfies, at the same time, the Abelian-like conservation law ∂μJμ=0 . The Abelian-like conservation law ∂μJμ=0 is also gauge-covariant. There are N2-1 conserved magnetic charges in the case of color S U (N ). The charge of each component of VNABI is quantized à la Dirac. The color-invariant eigenvalues λμ of VNABI also satisfy the Abelian conservation law ∂μλμ=0 and the magnetic charges of the eigenvalues are also quantized à la Dirac. If the color invariant eigenvalues condense in the QCD vacuum, each color component of the non-Abelian electric field Ea is squeezed by the corresponding color component of the solenoidal current Jμa. Then only the color singlets alone can survive as a physical state and non-Abelian color confinement is realized. This confinement picture is completely new in comparison with the previously studied monopole confinement scenario based on an Abelian projection after some partial gauge-fixing, where Abelian neutral states can survive as physical. To check if the scenario is realized in nature, numerical studies are done in the framework of lattice field theory by adopting pure S U (2 ) gauge theory for simplicity. Considering Jμ(x )=kμ(x ) in the continuum formulation, we adopt an Abelian-like definition of a monopole following DeGrand-Toussaint as a lattice version of VNABI, since the Dirac quantization condition of the magnetic charge is satisfied on lattice partially. To reduce severe lattice artifacts, we introduce various techniques of smoothing the thermalized vacuum. Smooth gauge fixings such as the maximal center gauge (MCG), block

A new approach to non-Abelian hydrodynamics

International Nuclear Information System (INIS)

Fernández-Melgarejo, Jose J.; Rey, Soo-Jong; Surówka, Piotr

2017-01-01

We present a new approach to describe hydrodynamics carrying non-Abelian macroscopic degrees of freedom. Based on the Kaluza-Klein compactification of a higher-dimensional neutral dissipative fluid on a manifold of non-Abelian isometry, we obtain a four-dimensional colored dissipative fluid coupled to Yang-Mills gauge field. We derive transport coefficients of resulting colored fluid, which feature non-Abelian character of color charges. In particular, we obtain color-specific terms in the gradient expansions and response quantities such as the conductivity matrix and the chemical potentials. We argue that our Kaluza-Klein approach provides a robust description of non-Abelian hydrodynamics, and discuss some links between this system and quark-gluon plasma and fluid/gravity duality.

A new approach to non-Abelian hydrodynamics

Energy Technology Data Exchange (ETDEWEB)

Fernández-Melgarejo, Jose J. [Center for the Fundamental Laws of Nature, Harvard University,Cambridge, MA 02138 (United States); Rey, Soo-Jong [School of Physics & Astronomy and Center for Theoretical Physics, Seoul National University,Seoul, 08826 (Korea, Republic of); Department of Fundamental Sciences, University of Science and Technology,Daejeon, 34113 (Korea, Republic of); Center for Gauge, Gravity & Strings, Institute for Basic Sciences,Daejeon, 34047 (Korea, Republic of); Surówka, Piotr [Center for the Fundamental Laws of Nature, Harvard University,Cambridge, MA 02138 (United States); Max-Planck-Institut für Physik (Werner-Heisenberg-Institut),Föhringer Ring 6, D-80805 Munich (Germany)

2017-02-23

We present a new approach to describe hydrodynamics carrying non-Abelian macroscopic degrees of freedom. Based on the Kaluza-Klein compactification of a higher-dimensional neutral dissipative fluid on a manifold of non-Abelian isometry, we obtain a four-dimensional colored dissipative fluid coupled to Yang-Mills gauge field. We derive transport coefficients of resulting colored fluid, which feature non-Abelian character of color charges. In particular, we obtain color-specific terms in the gradient expansions and response quantities such as the conductivity matrix and the chemical potentials. We argue that our Kaluza-Klein approach provides a robust description of non-Abelian hydrodynamics, and discuss some links between this system and quark-gluon plasma and fluid/gravity duality.

Stochastic quantization and gauge theories

International Nuclear Information System (INIS)

Kolck, U. van.

1987-01-01

Stochastic quantization is presented taking the Flutuation-Dissipation Theorem as a guide. It is shown that the original approach of Parisi and Wu to gauge theories fails to give the right results to gauge invariant quantities when dimensional regularization is used. Although there is a simple solution in an abelian theory, in the non-abelian case it is probably necessary to start from a BRST invariant action instead of a gauge invariant one. Stochastic regularizations are also discussed. (author) [pt

Tumbling in two djmensional gauge theories

International Nuclear Information System (INIS)

Banks, T.; Yankielowicz, S.; Frishman, Y.

1981-05-01

The ideas of Tumbling and Most Attractive Channel condensation are confronted in two dimensional chiral gauge theories. The performance of a gauge invariant regularization is first demonstrated. Exact results about the spectra in both abelian and non abelian cases are then found. These conflict with the predictions of Tumbling and MAC. (author)

Noncommuting fields and non-Abelian fluids

International Nuclear Information System (INIS)

Jackiw, R.

2004-01-01

The original ideas about noncommuting coordinates are recalled. The connection between U(1) gauge fields defined on noncommuting coordinates and fluid mechanics is explained. Non-Abelian fluid mechanics is described

Classical field theory on electrodynamics, non-Abelian gauge theories and gravitation

CERN Document Server

Scheck, Florian

2012-01-01

The book describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes wit...

Classical field theory on electrodynamics, non-abelian gauge theories and gravitation

CERN Document Server

Scheck, Florian

2018-01-01

Scheck’s successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell's theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell's theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell's theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary...

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.

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

Multiple normalized solutions for a planar gauged nonlinear Schrödinger equation

Science.gov (United States)

Luo, Xiao

2018-06-01

We study the existence, multiplicity, quantitative property and asymptotic behavior of normalized solutions for a gauged nonlinear Schrödinger equation arising from the Chern-Simons theory Δ u + ω u +|x|^2u+ λ ( {{h^2}(| x | )}/{{{| x | ^2}}} + \\int \\limits _{| x | }^{ + ∞} {{h(s)}/s} {u^2}(s)ds) u = {| u | ^{p - 2}}u,\\quad x\\in R^2, where ω \\in R, λ >0, p>4 and h(s) = 1/2\\int \\limits _0^s {r{u^2}(r)dr} . Combining constraint minimization method and minimax principle, we prove that the problem possesses at least two normalized solutions: One is a ground state and the other is an excited state. Furthermore, the asymptotic behavior and quantitative property of the ground state are analyzed.

Axial-gauge formulation of a three-dimensional field theory

International Nuclear Information System (INIS)

Hagen, C.R.

1985-01-01

Since the non-Abelian version of a recently formulated gauge theory in two spatial dimensions gives rise to a nonlinear constraint upon the fields in the radiation-gauge approach, one is motivated to attempt a description in terms of the axial gauge. This is accomplished in the Abelian version of the model, with results similar to those encountered in the radiation gauge. The non-Abelian case is then formally solved in the same gauge, it being subsequently shown, however, that the theory is not covariant. It is argued on the basis of perturbation theory that such noncovariance is a real effect which is not readily circumvented by modification of the field transformation properties

Quantum gauge freedom in very special relativity

Energy Technology Data Exchange (ETDEWEB)

Upadhyay, Sudhaker, E-mail: sudhakerupadhyay@gmail.com [Centre for Theoretical Studies, Indian Institute of Technology Kharagpur, Kharagpur-721302, West Bengal (India); Panigrahi, Prasanta K., E-mail: pprasanta@iiserkol.ac.in [Indian Institute of Science Education and Research Kolkata, Mohanpur 741246, West Bengal (India)

2017-02-15

We demonstrate Yokoyama gaugeon formalism for the Abelian one-form gauge (Maxwell) as well as for Abelian two-form gauge theory in the very special relativity (VSR) framework. In VSR scenario, the extended action due to introduction of gaugeon fields also possesses form invariance under quantum gauge transformations. It is observed that the gaugeon field together with gauge field naturally acquire mass, which is different from the conventional Higgs mechanism. The quantum gauge transformation implements a shift in gauge parameter. Further, we analyze the BRST symmetric gaugeon formalism in VSR which embeds only one subsidiary condition rather than two.

Abelian embedding formulation of the Stueckelberg model and its power-counting renormalizable extension

International Nuclear Information System (INIS)

Quadri, Andrea

2006-01-01

We elucidate the geometry of the polynomial formulation of the non-Abelian Stueckelberg mechanism. We show that a natural off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) differential exists allowing to implement the constraint on the σ field by means of BRST techniques. This is achieved by extending the ghost sector by an additional U(1) factor (Abelian embedding). An important consequence is that a further BRST-invariant but not gauge-invariant mass term can be written for the non-Abelian gauge fields. As all versions of the Stueckelberg theory, also the Abelian embedding formulation yields a nonpower-counting renormalizable theory in D=4. We then derive its natural power-counting renormalizable extension and show that the physical spectrum contains a physical massive scalar particle. Physical unitarity is also established. This model implements the spontaneous symmetry breaking in the Abelian embedding formalism

A higher form (of) mediation

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

The arithmetic of elliptic fibrations in gauge theories on a circle

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Grimm, Thomas W. [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 Munich (Germany); Institute for Theoretical Physics,Utrecht University, Leuvenlaan 4, 3584 CE Utrecht (Netherlands); Center for Extreme Matter and Emergent Phenomena,Utrecht University, Leuvenlaan 4, 3584 CE Utrecht (Netherlands); Kapfer, Andreas [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 Munich (Germany); Klevers, Denis [Theory Group, Physics Department, CERN,CH-1211, Geneva 23 (Switzerland)

2016-06-20

The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional Coulomb branch. Its existence is required by consistency with Higgs transitions from the non-Abelian theory to its Abelian phases in which it becomes the Mordell-Weil group. This hints towards the existence of a new underlying geometric symmetry.

The arithmetic of elliptic fibrations in gauge theories on a circle

Science.gov (United States)

Grimm, Thomas W.; Kapfer, Andreas; Klevers, Denis

2016-06-01

The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional Coulomb branch. Its existence is required by consistency with Higgs transitions from the non-Abelian theory to its Abelian phases in which it becomes the Mordell-Weil group. This hints towards the existence of a new underlying geometric symmetry.

The arithmetic of elliptic fibrations in gauge theories on a circle

International Nuclear Information System (INIS)

Grimm, Thomas W.; Kapfer, Andreas; Klevers, Denis

2016-01-01

The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional Coulomb branch. Its existence is required by consistency with Higgs transitions from the non-Abelian theory to its Abelian phases in which it becomes the Mordell-Weil group. This hints towards the existence of a new underlying geometric symmetry.

Renormalization and scaling behavior of non-Abelian gauge fields in curved spacetime

International Nuclear Information System (INIS)

Leen, T.K.

1983-01-01

In this article we discuss the one loop renormalization and scaling behavior of non-Abelian gauge field theories in a general curved spacetime. A generating functional is constructed which forms the basis for both the perturbation expansion and the Ward identifies. Local momentum space representations for the vector and ghost particles are developed and used to extract the divergent parts of Feynman integrals. The one loop diagram for the ghost propagator and the vector-ghost vertex are shown to have no divergences not present in Minkowski space. The Ward identities insure that this is true for the vector propagator as well. It is shown that the above renormalizations render the three- and four-vector vertices finite. Finally, a renormalization group equation valid in curved spacetimes is derived. Its solution is given and the theory is shown to be asymptotically free as in Minkowski space

Field-theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology, and beyond.

Science.gov (United States)

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.

Elastic gauge fields and Hall viscosity of Dirac magnons

Science.gov (United States)

Ferreiros, Yago; Vozmediano, María A. H.

2018-02-01

We analyze the coupling of elastic lattice deformations to the magnon degrees of freedom of magnon Dirac materials. For a honeycomb ferromagnet we find that, as happens in the case of graphene, elastic gauge fields appear coupled to the magnon pseudospinors. For deformations that induce constant pseudomagnetic fields, the spectrum around the Dirac nodes splits into pseudo-Landau levels. We show that when a Dzyaloshinskii-Moriya interaction is considered, a topological gap opens in the system and a Chern-Simons effective action for the elastic degrees of freedom is generated. Such a term encodes a phonon Hall viscosity response, entirely generated by quantum fluctuations of magnons living in the vicinity of the Dirac points. The magnon Hall viscosity vanishes at zero temperature, and grows as temperature is raised and the states around the Dirac points are increasingly populated.

Anomalous gauge theories revisited

International Nuclear Information System (INIS)

Matsui, Kosuke; Suzuki, Hiroshi

2005-01-01

A possible formulation of chiral gauge theories with an anomalous fermion content is re-examined in light of the lattice framework based on the Ginsparg-Wilson relation. It is shown that the fermion sector of a wide class of anomalous non-abelian theories cannot consistently be formulated within this lattice framework. In particular, in 4 dimension, all anomalous non-abelian theories are included in this class. Anomalous abelian chiral gauge theories cannot be formulated with compact U(1) link variables, while a non-compact formulation is possible at least for the vacuum sector in the space of lattice gauge fields. Our conclusion is not applied to effective low-energy theories with an anomalous fermion content which are obtained from an underlying anomaly-free theory by sending the mass of some of fermions to infinity. For theories with an anomalous fermion content in which the anomaly is cancelled by the Green-Schwarz mechanism, a possibility of a consistent lattice formulation is not clear. (author)

Analytical solution to DGLAP integro-differential equation in a simple toy-model with a fixed gauge coupling

Energy Technology Data Exchange (ETDEWEB)

Alvarez, Gustavo [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Concepcion Univ. (Chile). Dept. de Fisica; Cvetic, Gorazd [Univ. Tecnica Federico Santa Maria, Valparaiso (Chile). Dept. de Fisica; Kniehl, Bernd A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Kondrashuk, Igor [Univ. del Bio-Bio, Chillan (Chile). Grupo de Matematica Aplicada; Univ. del Bio-Bio, Chillan (Chile). Grupo de Fisica de Altas Energias; Parra-Ferrada, Ivan [Talca Univ. (Chile). Inst. de Matematica y Fisica

2016-11-15

We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not run. This may be N=4 supersymmetric gauge theory with softly broken supersymmetry, other finite supersymmetric gauge theory with lower level of supersymmetry, or topological Chern-Simons field theories. We maintain only one term in the splitting function of unintegrated gluon distribution and solve DGLAP analytically for this simplified splitting function. The solution is found by use of the Cauchy integral formula. The solution restricts form of the unintegrated gluon distribution as function of transfer momentum and of Bjorken x. Then we consider an almost realistic splitting function of unintegrated gluon distribution as an input to DGLAP equation and solve it by the same method which we have developed to solve DGLAP equation for the toy-model. We study a result obtained for the realistic gluon distribution and find a singular Bessel-like behaviour in the vicinity of the point x=0 and a smooth behaviour in the vicinity of the point x=1.

The valley method and its application to the instanton-induced phenomena in non-abelian gauge theories

International Nuclear Information System (INIS)

Khoze, V.V.

1991-06-01

The semiclassical evaluation of the functional integral on non-Abelian gauge theories is generalized by means of the so-called valley method. The physically very important example of the valley, the instanton-anti-instanton field configuration, is discussed in details and its contributions to the physical quantities for zero-temperature and for thermal field theories are investigated. The high-energy behaviour of the total cross-section σ Δ F for electroweak fermion number violating two particles collisions is studied using the optical theorem approach. The calculation is done at energies below the sphaleron mass (E<10TeV) where it leads to the most complete result for σ Δ F known to date. Some estimations and a qualitative physical picture are discussed for energies above the sphaleron mass for the confinement and Higgs phases of the gauge theory. The effects of instanton-anti-instanton interactions are also studied in thermal QCD. (au)

Towards Noncommutative Linking Numbers via the Seiberg-Witten Map

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H. García-Compeán

2015-01-01

Full Text Available Some geometric and topological implications of noncommutative Wilson loops are explored via the Seiberg-Witten map. In the abelian Chern-Simons theory on a three-dimensional manifold, it is shown that the effect of noncommutativity is the appearance of 6n new knots at the nth order of the Seiberg-Witten expansion. These knots are trivial homology cycles which are Poincaré dual to the higher-order Seiberg-Witten potentials. Moreover the linking number of a standard 1-cycle with the Poincaré dual of the gauge field is shown to be written as an expansion of the linking number of this 1-cycle with the Poincaré dual of the Seiberg-Witten gauge fields. In the process we explicitly compute the noncommutative “Jones-Witten” invariants up to first order in the noncommutative parameter. Finally in order to exhibit a physical example, we apply these ideas explicitly to the Aharonov-Bohm effect. It is explicitly displayed at first order in the noncommutative parameter; we also show the relation to the noncommutative Landau levels.

Topological insulators in cold-atom gases with non-Abelian gauge fields: the role of interactions

Energy Technology Data Exchange (ETDEWEB)

Orth, Peter Philipp [Institut fuer Theorie der Kondensierten Materie, Karlsruher Institut fuer Technologie, 76128 Karlsruhe (Germany); Cocks, Daniel; Buchhold, Michael; Hofstetter, Walter [Institut fuer Theoretische Physik, Goethe Universitaet, 60438 Frankfurt am Main (Germany); Rachel, Stephan [Department of Physics, Yale University, New Haven, Connecticut 06520 (United States); Le Hur, Karyn [Department of Physics, Yale University, New Haven, Connecticut 06520 (United States); Center for Theoretical Physics, Ecole Polytechnique, 91128 Palaiseau Cedex (France)

2012-07-01

With the recent technological advance of creating (non)-Abelian gauge fields for ultracold atoms in optical lattices, it becomes possible to study the interplay of topological phases and interactions in these systems. Specifically, we consider a spinful and time-reversal invariant version of the Hofstadter problem. In addition, we allow for a hopping term which does not preserve S{sub z} spin symmetry and a staggered sublattice potential. Without interactions, the parameters can be tuned such that the system is a topological insulator. Using a combination of analytical techniques and the powerful real-space dynamical mean-field (R-DMFT) method, we discuss the effect of interactions and determine the interacting phase diagram.

Equivalent D = 3 supergravity amplitudes from double copies of three-algebra and two-algebra gauge theories.

Science.gov (United States)

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.

Linking the Gauss-Bonnet-Chern theorem, essential HOPF maps and membrane solitons with exotic spin and statistics

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