Extended form method of antifield-BRST formalism for topological quantum field theories

TL;DR

This paper introduces an extended form method within the antifield-BRST formalism to efficiently construct BRST invariant actions for various topological quantum field theories, including BF and Chern-Simons theories.

Contribution

It provides a concise, direct approach to obtain BV actions for topological theories using extended forms that incorporate all ghosts and antifields.

Findings

Constructed BV actions for non-abelian BF theories in 4 and higher dimensions.

Derived BV action for Chern-Simons theory using the extended form method.

Explored an extension of 4D BF theory with a cosmological term and its relation to topological Yang-Mills theory.

Abstract

We present a concise method to construct a BRST invariant action for the topological quantum field theories in the Batalin-Vilkovisky antifield formalism. The BV action that is a solution for the master equation is directly obtained by means of the extended forms that involve all the required ghosts and antifields. The BV actions for the non-abelian $BF$ theories (in 4 and higher dimensions) and the Chern-Simons theory are constructed by means of the extended form method. An extension of the $BF$ theory in 4-dimensions to include a ``cosmological term'' is also examined and the close connection with the topological Yang-Mills theory is indicated.