G/G models as the strong coupling limit of topologically massive gauge theory

TL;DR

This paper demonstrates that the strong coupling limit of topologically massive gauge theory can be analyzed using the $G_k/G$ topological field theory, enabling analytical computation of correlators and effective potentials.

Contribution

It establishes an equivalence between the strong coupling limit of gauge theory and the $G_k/G$ model, providing new analytical tools for studying non-perturbative effects.

Findings

Correlators in the strong coupling limit are analytically computable.

The effective potential for Polyakov loops is derived at one-loop order.

The theory exhibits a deconfined phase at strong coupling.

Abstract

We show that the problem of computing the vacuum expectation values of gauge invariant operators in the strong coupling limit of topologically massive gauge theory is equivalent to the problem of computing similar operators in the $G_k/G$ model where $k$ is the integer coefficient of the Chern-Simons term. The $G_k/G$ model is a topological field theory and many correlators can be computed analytically. We also show that the effective action for the Polyakov loop operator and static modes of the gauge fields of the strongly coupled theory at finite temperature is a perturbed, non-topological $G_k/G$ model. In this model, we compute the one loop effective potential for the Polyakov loop operators and explicitly construct the low-lying excited states. In the strong coupling limit the theory is in a deconfined phase.