BRST quantization of topological field theories

Abstract

We consider in detail the construction of a variety of topological quantum field theories through BRST quantization. In particular, we show that supersymmetric quantum mechanics on an arbitrary riemannian manifold can be obtained as the BRST quantization of a purely bosonic theory. The introduction of a new local symmetry allows for the possibility of different gauge choices, and we show how this freedom can simplify the evaluation of the Witten index in certain cases. Topological sigma models are also constructed via the same mechanism. In three dimensions, we consider a Yang-Mills-Higgs model related to the four-dimensional TQFT of Witten.