Geometrical Interpretation of BRST Symmetry in Topological Yang-Mills-Higgs Theory

TL;DR

This paper unifies the description of topological Yang-Mills-Higgs and Yang-Mills theories across dimensions using superconnections, revealing the geometric origin of BRST symmetry through Bianchi identities.

Contribution

It extends the superconnection framework to include multiple topological theories and interprets BRST symmetry geometrically via Bianchi identities.

Findings

Unified geometric framework for topological theories across dimensions

Derived BRST and anti-BRST transformations from superconnections

Provided a geometric interpretation of BRST symmetry

Abstract

We study topological Yang-Mills-Higgs theories in two and three dimensions and topological Yang-Mills theory in four dimensions in a unified framework of superconnections. In this framework, we first show that a classical action of topological Yang-Mills type can provide all three classical actions of these theories via appropriate projections. Then we obtain the BRST and anti-BRST transformation rules encompassing these three topological theories from an extended definition of curvature and a geometrical requirement of Bianchi identity. This is an extension of Perry and Teo's work in the topological Yang-Mills case. Finally, comparing this result with our previous treatment in which we used the ``modified horizontality condition", we provide a meaning of Bianchi identity from the BRST symmetry viewpoint and thus interpret the BRST symmetry in a geometrical setting.