A General Solution of the BV-Master Equation and BRST Field Theories

TL;DR

This paper develops a general framework for solving the BV-master equation applicable to a broad class of gauge theories, including Chern-Simons and BRST field theories, by establishing key conditions on gauge generators.

Contribution

It introduces a universal condition on gauge generators ensuring the BV-master equation solution is straightforward, extending applicability to BRST theories.

Findings

Applicable to Chern-Simons theory in any odd dimension

Formalism bridges BV and BRST field theories

Provides a general condition for gauge generators

Abstract

For a class of first order gauge theories it was shown that the proper solution of the BV-master equation can be obtained straightforwardly. Here we present the general condition which the gauge generators should satisfy to conclude that this construction is relevant. The general procedure is illustrated by its application to the Chern-Simons theory in any odd-dimension. Moreover, it is shown that this formalism is also applicable to BRST field theories, when one replaces the role of the exterior derivative with the BRST charge of first quantization.