On Auxiliary Fields in BF Theories

TL;DR

This paper explores the structure of auxiliary fields in non-Abelian BF theories across various dimensions, modifying the BRST operator to achieve an invariant quantum action with closed algebra.

Contribution

It introduces a method to incorporate auxiliary fields that close the BRST algebra, enabling an invariant extension of the classical action in BF theories.

Findings

Auxiliary fields close the BRST algebra in non-Abelian BF theories.

Modified BRST operator yields an on-shell invariant quantum action.

Provides a systematic approach for auxiliary fields in arbitrary dimensions.

Abstract

We discuss the structure of auxiliary fields for non-Abelian BF theories in arbitrary dimensions. By modifying the classical BRST operator, we build the on-shell invariant complete quantum action. Therefore, we introduce the auxiliary fields which close the BRST algebra and lead to the invariant extension of the classical action.