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

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. PACS number(s): 02.40.-k, 11.15.-q, 11.30.-j † Electronic-mail: [email protected]