Abelian topologically massive gauge theories (TMGT) provide a topological mechanism to generate mass for any p-tensor boson in any dimension. Within the Hamiltonian formulation, the embedded topological field theory (TFT) is not made manifest. We therefore introduce a gauge invariant factorization of the classical phase space in two orthogonal sectors. The first of these sectors is that of gauge invariant dynamical variables with massive excitations. The second is that of a decoupled TFT. Through canonical quantization, a factorization of quantum states arises, enabling the projection from TMGT onto topological quantum field theories in a most transparent way.
We show that the renormalized vacuum expectation value of the Wilson loop for topologically massive abelian gauge theory in $\RR^3$ can be defined so that its large-mass limit be the renormalized vacuum expectation value of the Wilson loop for abelian Chern-Simons theory also in $\RR^3$.
We study the relationship between three non-Abelian topologically massive gauge theories, viz. the naive non-Abelian generalization of the Abelian model, Freedman-Townsend model and the dynamical 2-form theory, in the canonical framework. Hamiltonian formulation of the naive non-Abelian theory is presented first. The other two non-Abelian models are obtained by deforming the constraints of this model. We study the role of the auxiliary vector field in the dynamical 2-form theory in the canonical framework and show that the dynamical 2-form theory cannot be considered as the embedded version of…
An irreducible Hamiltonian BRST approach to topologically coupled p- and (p+1)-forms is developed. The irreducible setting is enforced by means of constructing an irreducible Hamiltonian first-class model that is equivalent from the BRST point of view to the original redundant theory. The irreducible path integral can be brought to a manifestly Lorentz covariant form.
We analyse the equivalence between topologically massive gauge theory (TMGT) and different formulations of non-topologically massive gauge theories (NTMGTs) in the canonical approach. The different NTMGTs studied are Stückelberg formulation of (A) a first order formulation involving one and two form fields, (B) Proca theory, and (C) massive Kalb-Ramond theory. We first quantise these reducible gauge systems by using the phase space extension procedure and using it, identify the phase space variables of NTMGTs which are equivalent to the canonical variables of TMGT and show that under this the …
We start with a new first order gauge non-invariant formulation of massive spin-one theory and map it to a reducible gauge theory viz; abelian $B{\wedge}F$ theory by the Hamiltonian embedding procedure of Batalin, Fradkin and Tyutin(BFT). This equivalence is shown from the equations of motion of the embedded Hamiltonian. We also demonstrate that the original gauge non-invariant model and the topologically massive gauge theory can both be obtained by suitable choice of gauges, from the phase space partition function of the emebedded Hamiltonian, proving their equivalence. Comparison of the firs…
We thereby prove that a large class of topologically massive theories of the Cremmer-Scherk-Kalb-Ramond-type in any $d$ dimensions corresponds to gauge non-invariant first-order theories that can be interpreted as self-dual models.
We discuss three mathematical structures which arise in topologically massive abelian gauge theory. First, the euclidean topologically massive abelian gauge theory defines a contact structure on a manifold. We briefly discuss three solutions and the related contact structures on the flat 3-torus, the AdS space, the 3-sphere which respectively correspond to Bianchi type I, VIII, IX spaces. We also present solutions on Bianchi type II, VI and VII spaces. Secondly, we discuss a family of complex (anti-)self-dual solutions of the euclidean theory in cartesian coordinates on R3 which are given by (…
We study topologically massive (B \wedge F) Abelian and non-Abelian gauge theories in four dimensions, and reduce them to three dimensions by assuming that the fields do not propagate in one of the spatial directions. For certain gauge choices the reduced theories are the Jackiw-Pi models of massive gauge fields.
We demonstrate the existence of the nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the four (3 + 1)-dimensional (4D) topologically massive Abelian U(1) gauge theory that is described by the coupled Lagrangian densities (which incorporate the celebrated (B \wedge F) term). The absolute anticommutativity of the (anti-) BRST symmetry transformations is ensured by the existence of a Curci-Ferrari type restriction that emerges from the superfield formalism as well as from the equations of motion that are derived from the above coup…
A dynamical non-Abelian 2-form gauge theory (with B \wedge F term) is endowed with the "scalar" and "vector" gauge symmetry transformations. In our present endeavor, we exploit the latter gauge symmetry transformations and perform the Becchi-Rouet-Stora-Tyutin (BRST) analysis of the four (3 + 1)-dimensional (4D) topologically massive non-Abelian 2-form gauge theory. We demonstrate the existence of some novel features that have, hitherto, not been observed in the context of BRST approach to 4D (non-)Abelian 1-form as well as Abelian 2-form and 3-form gauge theories. We comment on the difference…
The non-abelian version of the self-dual model proposed by Townsend, Pilch and van Nieuwenhuizen presents some well known difficulties not found in the abelian case, such as well defined duality operation leading to self-duality and dual equivalence with the Yang-Mills-Chern-Simons theory, for the full range of the coupling constant. These questions are tackled in this work using a distinct gauge lifting technique that is alternative to the master action approach first proposed by Deser and Jackiw. The master action, which has proved useful in exhibiting the dual equivalence between theories i…
The set of degenerate ground states of an arbitrary nonabelian topologically massive gauge theory is shown to be in one-to-one correspondence with the Hilbert space of the associated pure Chern-Simons theory. (Paper is being withdrawn: original conclusion is incorrect for the nonabelian case. For a correct treatment, see M. Asorey, S. Carlip, and F. Falceto, hep-th/9304081.)
In an abelian topologically massive gauge theory, any eigenstate of the Hamiltonian can be decomposed into a factor describing massive propagating gauge bosons and a Chern-Simons wave function describing a set of nonpropagating ``topological'' excitations. The energy depends only on the propagating modes, and energy eigenstates thus occur with a degeneracy that can be parametrized by the Hilbert space of the pure Chern-Simons theory. We show that for a {\em nonabelian} topologically massive gauge theory, this degeneracy is lifted: although the Gauss law constraint can be solved with a similar …
We establish a duality between massive fermions coupled to topologically massive gravity (TGM) in $d=3$ space-time dimensions and a purely gravity theory which also will turn out to be a TGM theory but with different parameters: the original graviton mass in the TGM theory coupled to fermions picks-up a contribution from fermion bosonization. We obtain explicit bosonization rules for the fermionic currents and for the energy-momentum-tensor showing that the identifications do not depend explicitly on the parameters of the theory. These results are the gravitational analog of the results for $2…
A Lagrangian formulation describing the electromagnetic interaction - mediated by topologically massive vector bosons - between charged, spin-(1/2) fermions with an abelian magnetic monopole in a curved spacetime with non-minimal coupling and torsion potential is presented. The covariant field equations are obtained. The issue of coexistence of massive photons and magnetic monopoles is addressed in the present framework. It is found that despite the topological nature of photon mass generation in curved spacetime with isotropic dilaton field, the classical field theory describing the nonrelati…
We apply the well-established techniques of geometrical superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism in the context of four (3 + 1)-dimensional (4D) dynamical non-Abelian 2-form gauge theory by exploiting its inherent "scalar" and "vector" gauge symmetry transformations and derive the corresponding off-shell nilpotent and absolutely anticommuting BRST and anti-BRST symmetry transformations. Our approach leads to the derivation of three (anti-) BRST invariant Curci-Ferrari (CF)-type restrictions that are found to be responsible for the absolute anticommutativity of the BRST…
Schwinger pair production is analyzed in a BPST instanton background and in its SL$(2,\mathbb{C})$ complex extension for complex scalar particles. A non-Abelian extension of the worldline instanton method is utilized, wherein Wong's equations in a coherent state picture adopted for SL$(2,\mathbb{C})$ are solved in Euclidean spacetime. While pair production is not predicted in the BPST instanton, a complex extension of the BPST instanton, existing as parallel fields in Minkowski spacetime, is shown to decay via the Schwinger effect.
We investigate in which sense, at the linearized level, one can extend the 3D topologically massive gravity theory beyond three dimensions. We show that, for each k=1,2,3... a free topologically massive gauge theory in 4k-1 dimensions can be defined describing a massive "spin-2" particle provided one uses a non-standard representation of the massive "spin-2" state which makes use of a two-column Young tableau where each column is of height 2k-1. We work out the case of k=2, i.e. 7D, and show, by canonical analysis, that the model describes, unitarily, 35 massive "spin-2" degrees of freedom. Th…
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 has been extended to topologically massive gauge theories (TMGT) in any dimension. This Letter introduces an unconventional approach to the construction of this type of duality through a reparametrisation of the master theory action. The dual action thereby obtained preserves the same gauge symmetry structure as the original theory. Furthermore, the dual action is factorised into a propagating sector of massive gauge invariant variables and a sector…
We consider three-dimensional maximally superconformal Bagger-Lambert-Gustavsson (BLG) theory and its topologically gauged version (constructed recently in arXiv:0809.4478 [hep-th]) in the light-cone gauge. After eliminating the entire Chern-Simons gauge field, the ungauged BLG theory looks more conventional and, apart from the order of the interaction terms, resembles N=4 super-Yang-Mills theory in four dimensions. The light-cone superspace version of the BLG theory is given to quadratic and quartic order and some problems with constructing the sixth order interaction terms are discussed. In …
Topologically charged black holes in a theory with a 2-form coupled to a non-abelian gauge field are investigated. It is found that the classification of the ground states is similar to that in the theory of non-abelian discrete quantum hair.
We discuss locally Weyl (scale) covariant generalisations of gravitational theories using Riemann-Cartan-Weyl space-times in arbitrary dimensions. We demonstrate the procedure of Weyl gauging on two examples in particular: General relativity, and topologically massive gravity in three dimensions.
By coupling {\cal N}=8 superconformal matter to {\cal N}=8 superconformal Chern-Simons gravity in three dimensions we obtain theories with novel terms in the scalar potential leading to AdS_3 solutions and superconformal symmetry breaking. If we start from the theory derived by Bagger, Lambert and Gustavsson, our coupled theory either inherits the SO(4) gauge group or reduces it to SO(3). If the construction is instead based on a free matter theory we find that the gravitational topological gauging also requires the introduction of a Chern-Simons gauge sector resulting in a consistent theory f…
We apply differential renormalization method to the study of three-dimensional topologically massive Yang-Mills and Chern-Simons theories. The method is especially suitable for such theories as it avoids the need for dimensional continuation of three-dimensional antisymmetric tensor and the Feynman rules for three-dimensional theories in coordinate space are relatively simple. The calculus involved is still lengthy but not as difficult as other existing methods of calculation. We compute one-loop propagators and vertices and derive the one-loop local effective action for topologically massive …
We discuss the generalization of Abelian Chern-Simons theories when $θ$-angles and magnetic monopoles are included. We map sectors of two dimensional Conformal Field Theories into these three dimensional theories.
We compute the topologically twisted index for general $\mathcal{N} = 2$ supersymmetric field theories on $\mathbb{H}_2\times S^1$. We also discuss asymptotically $AdS_4$ magnetically charged black holes with hyperbolic horizon, in four-dimensional $\mathcal{N} = 2$ gauged supergravity. With certain assumptions, put forward by Benini, Hristov and Zaffaroni, we find precise agreement between the black hole entropy and the topologically twisted index, for $ABJM$ theories.
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 factorisation of phase space into two orthogonal sectors is feasible. …
A pure Dirac's method for abelian and non-abelian massive theories in three dimensions is performed. Our analysis is developed on the extended phase space reporting the relevant structure of the theories, namely, the extended action, the extended Hamiltonian, the full structure of the constraints and the counting of degrees of freedom. In addition, we compare our results with those found in the literature.
It is demonstrated that in the (2+1)-dimensional topologically massive gauge theories an agreement of the Pauli-Villars regularization scheme with the other schemes can be achieved by employing pairs of auxiliary fermions with the opposite sign masses. This approach does not introduce additional violation of discrete (P and T) symmetries. Although it breaks the local gauge symmetry only in the regulator fields' sector, its trace disappears completely after removing the regularization as a result of superrenormalizability of the model. It is shown also that analogous extension of the Pauli-Vill…
Using the principles of the modern scattering amplitudes programme, we develop a formalism for constructing the amplitudes of three-dimensional topologically massive gauge theories and gravity. Inspired by recent developments in four dimensions, we construct the three-dimensional equivalent of $x$-variables for conserved matter currents coupled to topologically massive gauge bosons or gravitons. Using these, we bootstrap various matter-coupled gauge-theory and gravitational scattering amplitudes, and conjecture that topologically massive gauge theory and topologically massive gravity are relat…
We construct a novel topologically massive abelian Chern-Simons gauge theory with 32 global supersymmetries in three spacetime dimensions. In spite of the 32 supercharges, the theory exhibits massive excitations only up to spin 1. The possibility of such a multiplet shortening is due to the presence of non-central R-symmetry generators in the Poincare superalgebra, whose supermultiplets are determined.
In the pseudo-euclidean metrics Chern-Simons gauge theory in the infrared region is found to be associated with dissipative dynamics. In the infrared limit the Lagrangian of 2+1 dimensional pseudo-euclidean topologically massive electrodynamics has indeed the same form of the Lagrangian of the damped harmonic oscillator. On the hyperbolic plane a set of two damped harmonic oscillators, each other time-reversed, is shown to be equivalent to a single undamped harmonic oscillator. The equations for the damped oscillators are proven to be the same as the ones for the Lorentz force acting on two pa…
We study six-dimensional N=(1,0) supergravity theories with abelian, as well as non-abelian, gauge group factors. We show that for theories with fewer than nine tensor multiplets, the number of possible combinations of gauge groups - including abelian factors - and non-abelian matter representations is finite. We also identify infinite families of theories with distinct U(1) charges that cannot be ruled out using known quantum consistency conditions, though only a finite subset of these can arise from known string constructions.
The structure of extrinsic defects in topologically ordered states of matter is host to a rich set of universal physics. Extrinsic defects in 2+1 dimensional topological states include line-like defects, such as boundaries between topologically distinct states, and point-like defects, such as junctions between different line defects. Gapped boundaries in particular can themselves be \it topologically \rm distinct, and the junctions between them can localize topologically protected zero modes, giving rise to topological ground state degeneracies and projective non-Abelian statistics. In this pa…
There is a natural way to study the long distance interactions of gauge theories in the electric (momentum) representation. Here, the main ideas are presented for the Abelian and Yang-Mills gauge theories emphasizing on the structure and the advantages of this approach.
In this work we show a dualization process of a non-Abelian model with an antisymmetric tensor gauge field in a three-dimensional space-time. We have constructed a non-Abelian gauge invariant Stückelberg-like master action, and a duality between a non-Abelian topologically massive $B\wedgeϕ$ model and a non-Abelian massive scalar action, which leads us to a Klein-Gordon-type action when we consider a particular case.
In this paper a class of multi-Chern-Simons field theories which is relevant to the statistical mechanics of polymer systems is investigated. Motivated by the problems which one encounters in the treatment of these theories, a general procedure is presented to eliminate the Chern-Simons fields from their action. In this way it has been possible to derive an expression of the partition function of topologically linked polymers which depends explicitly on the topological numbers and does not have intractable nonlocal terms as it happened in previous approaches. The new formulation of multi-Chern…
Einstein- Schroedinger (ES) non-symmetric theory has been extended to accommodate the Abelian and non-Abelian gauge theories of dyons in terms of the quaternion-octonion metric realization. Corresponding covariant derivatives for complex, quaternion and octonion spaces in internal gauge groups are shown to describe the consistent field equations and generalized Dirac equation of dyons. It is also shown that quaternion and octonion representations extend the so-called unified theory of gravitation and electromagnetism to the Yang-Mill's fields leading to two SU(2) gauge theories of internal spa…
Contour gauges are discussed in the framework of canonical formalism. We find flux operator algebras with the structure constants of underlying Yang-Mills theory.
We explore topologically massive gauge theories using the covariant colour kinematics duality recently introduced by Cheung and Mangan. We show that the massive bi-adjoint scalar field is simply related to topologically massive gauge theory by the duality, and that enacting the same duality on the gauge theory produces topologically massive gravity coupled to a scalar or, equivalently, an antisymmetric field. We also show that different choices for the replacement of the colour structure constants with kinematic structure constants lead to different theories, including a topologically massive …
The quantum Yang-Mills theory describing dual ($\tilde g$) and non-dual ($g$) charges and revealing the generalized duality symmetry was developed by analogy with the Zwanziger formalism in QED.
We find non-covariant local symmetries in the Abelian gauge theories. The Nöther charges generating these symmetries are nilpotent as BRST charges, and they impose constraints on the physical states.
Recently Seiberg has conjectured a duality symmetry connecting different theories of the supersymmetric QCD type. We provide support for this conjecture by analyzing a flat direction of the theory along which the two dual theories go over to the same theory in the IR.
A possible mechanism accounting for monopole configurations in continuum Yang-Mills theories is discussed. The presence of the gauge fixing term is taken into account.
Abelian Gauge Theories are quantized in a geometric representation that generalizes the Loop Representation and treates electric and magnetic operators on the same footing. The usual canonical algebra is turned into a topological algebra of non local operators that resembles the order-disorder dual algebra of 't Hooft. These dual operators provide a complete description of the physical phase space of the theories.
NON-ABELIAN TODA THEORIES are shown to provide EXACTLY SOLVABLE conformal systems in the presence of a BLACK HOLE which may be regarded as describing a string propagating in target space with a black-hole metric. These theories are associated with non-canonical $\bf Z$-gradations of simple algebras, where the gradation-zero subgroup is non-abelian. They correspond to gauged WZNW models where the gauge group is nilpotent and are thus basically different from the ones currently considered following Witten. The non-abelian Toda potential gives a cosmological term which may be exactly integrated a…
We clarify the physical origin of the difference between gauge properties of conserved currents in abelian and nonabelian theories. In the latter, but not in the former, such currents can always be written on shell as gauge invariants modulo identically conserved, superpotential, terms. For the ``isotopic" vector and the stress tensor currents of spins 1 and 2 respectively, we explain this difference by the fact that the non-abelian theories are just the self-coupled versions of the abelian ones using these currents as sources. More precisely, we indicate how the self-coupling turns the non-in…
We discuss the evaluation of observables in two-dimensional conformal field theory using the topological membrane description. We show that the spectrum of anomalous dimensions can be obtained perturbatively from the topologically massive quantum field theories by computing radiative corrections to Aharonov-Bohm scattering amplitudes for dynamical charged matter fields. The one-loop corrections in the case of topologically massive Yang-Mills theory are shown to coincide with the scaling dimensions of the induced ordinary and supersymmetric WZNW models. We examine the effects of the dressing of…
In this work we have shown that it is possible to construct non-Abelian field theories employing, in a systematic way, the Faddeev-Jackiw symplectic formalism. This approach follows two steps. In the first step, the original Abelian fields are modified in order to introduce the non-Abelian algebra. After that, the Faddeev-Jackiw method is implemented and the gauge symmetry relative to some non-Abelian symmetry group, is introduced through the zero-mode of the symplectic matrix. We construct the SU(2) and SU(2)xU(1) Yang-Mills theories having as starting point the U(1) Maxwell electromagnetic t…
We show for the case of interacting massless vector bosons, how the structure of Yang-Mills theories emerges automatically from a more fundamental concept, namely perturbative quantum gauge invariance. It turns out that the coupling in a non-abelian gauge theory is necessarily of Yang-Mills type plus divergence- and coboundary couplings. The extension of the method to massive gauge theories is briefly discussed.
A basis of Lorentz and gauge-invariant monomials in non--Abelian gauge theories with matter is described, applicable for the inverse mass expansion of effective actions. An algorithm to convert an arbitrarily given invariant expression into a linear combination of the basis elements is presented. The linear independence of the basis invariants is proven.
In this paper we investigate the canonical quantization of a non-Abelian topologically massive Chern-Simons theory in which the gauge fields are minimally coupled to a multiplet of scalar fields in such a way that the gauge symmetry is spontaneously broken. Such a model produces the Chern-Simons-Higgs mechanism in which the gauge excitations acquire mass both from the Chern-Simons term and from the Higgs-Kibble effect. The symmetry breaking is chosen to be only partially broken, in such a way that in the broken vacuum there remains a residual non-Abelian symmetry. We develop the canonical oper…
Consistent couplings between an Abelian gauge field and three types of matter fields are investigated by means of the Hamiltonian BRST deformation theory based on cohomological techniques. In this manner, scalar electrodynamics, the Stuckelberg theory for Abelian zero- and one-forms, respectively, spinor electrodynamics, are inferred.
We study the interaction of non-Abelian topological $BF$ theories defined on two dimensional manifolds with point sources carrying non-Abelian charges. We identify the most general solution for the field equations on simply and multiply connected two-manifolds. Taking the particular choice of the so-called extended Poincaré group as the gauge group we discuss how recent discussions of two dimensional gravity models do fit in this formalism.
We show the derivation of the self-duality relation of abelian higher-form gauge field strength in the topologically nontrivial spacetime background. The so-called Pasti-Sorokin-Tonin action for the self-dual abelian gauge field assumes that the spacetime topology is trivial to derive the self-duality relation using a gauge transformation of the action. In this paper we find a new gauge transformation of the same theory and show that this new gauge transformation enables us to derive the self-duality relation even in the topologically nontrivial spacetime background.
In this note we review the construction of topologically gauged M2 branes with 6 supersymmetries and discuss some of its properties. This is done using the 3-algebra formulation thereby covering all possible gauge groups. We will elaborate upon 1) the fundamental identity and its solutions noting, provided these gauged theories describe stacks of branes, the case of a single brane, 2) the chiral point solution to the field equations (occuring even for a single brane) that breaks the superconformal symmetries down to those of AdS_3 (TMG) supergravity, 3) physical parameters and how they scale i…
Non-Abelian BPS vortex solutions are constructed in N=2 theories with gauge groups SO(N)\times U(1). The model has N_f flavors of chiral multiplets in the vector representation of SO(N), and we consider a color-flavor locked vacuum in which the gauge symmetry is completely broken, leaving a global SO(N)_{C+F} diagonal symmetry unbroken. Individual vortices break this symmetry, acquiring continuous non-Abelian orientational moduli. By embedding this model in high-energy theories with a hierarchical symmetry breaking pattern such as SO(N+2) --> SO(N)\times U(1) --> 1, the correspondence between …
The algebraic conditions that specific gauged G/H-WZW model have to satisfy in order to give rise to Non-Abelian Toda models with singular metric with or without torsion are found. The classical algebras of symmetries corresponding to grade one rank 2 and 3 singular NA-Toda models are derived.
A manifestly Lorentz invariant effective action for Yang-Mills theory depending only on commuting fields is constructed. This action posesses a bosonic symmetry, which plays a role analogous to the BRST symmetry in the standard formalism.
We study the mirror symmetry of abelian 3d $\mathcal{N}=2$ theories with mixed Chern-Simons levels by turning them into $\mathcal{T}_{A,N}$ theories that are defined as $N$ copies of $U(1)-[1]$ theory coupled together by mixed Chern-Simons levels $k_{ij}$. We find that $\mathcal{T}_{A,N}$ theories have many mirror dual theories with different mixed CS levels and FI parameters. As an example, we analyze $U(1)_k+ N_C \,\mathbf{C} + N_{AC} \, \mathbf{AC}$ theories by transforming these theories into certain $\mathcal{T}_{A,N}$ theories and find many equivalent effective Chern-Simons levels. Final…
