Topologically massive gauge theories and their dual factorized gauge-invariant formulation

Abstract

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 with gauge variant variables defining a pure topological field theory. Combining results obtained within the Lagrangian and Hamiltonian formulations, a new completed structure for a gauge invariant dual factorisation of TMGT is thus achieved.

An analysis of the first-order form of gauge theories

“…Further discussion of how to rewrite the action for Abelian gauge fields when topological actions also occur appear in refs. [19,20]. An action for the Chern-Simons model when accompanied by a Stueckelberg mass term is in ref.…”

“…refs. [19,20]. An action for the Chern-Simons model when accompanied by a Stueckelberg mass term is in ref.…”

Non-perturbative dynamics, pair condensation, confinement and dynamical masses in massless QED2+1

“…factorisation of the physical degrees of freedom [11,12] and considers the dynamics of fermions "dressed" by their electric field, as first introduced by Dirac [13]. The dressing of physical charges was elaborated further in [14], for instance, and was shown to greatly improve the soft dynamics [15].…”

Dressed fermions, modular transformations and bosonization in the compactified Schwinger model

“…Obviously composite quantum operators need to be carefully defined in order to preserve the modular gauge symmetry in a manifest way (see (13); that a regularization prescription also preserves gauge invariance in a manifest way under local small transformations is readily checked). Let us first consider the bilinear fermion contributions to the first-class Hamiltonian H, which need to be properly defined to ensure both finite matrix elements and a ground state of finite energy, given that b m and d m are taken to be annihilators of a fermionic Fock vacuum, with b † m and d † m acting as creators.…”

“…However, in the non-perturbative domain, any gauge fixing procedure usually induces so-called Gribov problems. To avoid these difficulties it is possible to apply in the case of this model a manifestly gauge-invariant quantization free of gauge fixing, but rather by relying on a gauge-invariant factorization of the physical degrees of freedom [12,13]. Furthermore, invariance under 'large gauge transformations' is made explicit; space compactification into a circle makes possible the factorization of gauge symmetries into 'small' and 'large' gauge transformations.…”