Complex geometrical interpretation of BRST algebra in topological Yang-Mills theory

Abstract

We show that the BRST and anti-BRST algebra can be obtained by constructing a complex vector bundle over (M x X), where M is the real four-manifold and X an additional complex manifold. Witten's BRST algebra is derived from a hermitian holomorphic vector bundle, and the complex manifold X can be identified with the instanton moduli space.