Geometrical interpretation of BRST symmetry in topological Yang–Mills–Higgs theory

Abstract

We study the topological Yang–Mills–Higgs theories in two and three dimensions and the 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 Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST transformation rules encompassing these three topological theories from an extended definition of curvature and a geometrical requirement of the 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 the Bianchi identity from the BRST symmetry viewpoint and thus interpret the BRST symmetry in a geometrical setting.