Batalin-Vilkovisky quantization of symmetric Chern-Simons theory

TL;DR

This paper applies the Batalin-Vilkovisky quantization to symmetric Chern-Simons theory, showing its gauge fixing reduces to the standard form and its renormalizability matches the original theory.

Contribution

It introduces a covariant formulation of symmetric Chern-Simons theory and demonstrates its equivalence and renormalizability properties using BV quantization.

Findings

Gauge fixed action reduces to standard Chern-Simons form

Renormalizability is preserved in the symmetric formulation

Field redefinition connects symmetric and standard Chern-Simons actions

Abstract

We study the manifestly covariant three-dimensional symmetric Chern-Simons action in terms of the Batalin-Vilkovisky quantization method. We find that the Lorentz covariant gauge fixed version of this action is reduced to the usual Chern-Simons type action after a proper field redefinition. Furthermore, the renormalizability of the symmetric Chern-Simons theory turns out to be the same as that of the original Chern-Simons theory.