Equivalence of Chern-Simons gauge theory and WZNW model using a BRST symmetry

TL;DR

This paper demonstrates a straightforward and general method to establish the equivalence between Chern-Simons gauge theory and the WZNW model on a boundary using BRST symmetry, avoiding complex constraint solving.

Contribution

It introduces a novel approach based on restoring gauge invariance with BRST symmetry, simplifying the proof of equivalence without fixing gauges or boundary conditions.

Findings

Establishes a simple, general proof of the Chern-Simons and WZNW equivalence.

Avoids solving constraints or fixing gauges in the equivalence proof.

Provides a method applicable to theories with boundaries using BRST symmetry.

Abstract

The equivalence between the Chern-Simons gauge theory on a three-dimensional manifold with boundary and the WZNW model on the boundary is established in a simple and general way using the BRST symmetry. Our approach is based on restoring gauge invariance of the Chern-Simons theory in the presence of a boundary. This gives a correspondence to the WZNW model that does not require solving any constraints, fixing the gauge or specifying boundary conditions.