Worldline Approach of Topological BF Theory

TL;DR

This paper develops a worldline formalism for topological non-abelian BF theory, linking BRST cohomology to de Rham cohomology, and constructs a second-quantized action satisfying the BV master equation.

Contribution

It introduces a novel worldline approach to topological BF theory, providing a minimal BV solution and clarifying the geometric role of antifields and ghosts.

Findings

BRST cohomology corresponds to de Rham cohomology

Constructed a second-quantized BF action satisfying BV master equation

Revealed geometric interpretation of antifields and ghosts

Abstract

We present a worldline description of topological non-abelian BF theory in arbitrary space-time dimensions. It is shown that starting with a trivial classical action defined on the worldline, the BRST cohomology has a natural representation as the sum of the de Rham cohomology. Based on this observation, we construct a second-quantized action of the BF theory. Interestingly enough, this theory naturally gives us a minimal solution to the Batalin-Vilkovisky master equation of the BF theory. Our formalism sheds some light not only on an interplay between the Witten-type and the Schwarz-type topological quantum field theories but also on the role of the Batalin-Vilkovisky antifields and ghosts as geometrical and elementary objects.