Topological Yang-Mills theory is abelian chiral anomaly in superspace

Abstract

Ghost moments of the BRST operator in the four-dimensional topological Yang-Mills theory determine the Gauss law generator of the Parisi-Sourlas extended Yang-Mills theory, with the superspace curvature two-form reproducing BRST transformations of the component fields. The superspace generalization of the abelian chiral anomaly contains Donaldson's invariants when expanded in the supercoordinates, and its cohomological nontriviality follows from standard arguments: The chiral anomaly is the superspace exterior differential of the Parisi-Sourlas generalized Chern-Simons three-form which fails to remain invariant under superspace gauge transformations.