Basic and equivariant cohomology in balanced topological field theory

Abstract

We present a detailed algebraic study of the N=2 cohomological set-up describing the balanced topological field theory of Dijkgraaf and Moore. We emphasize the role of N=2 topological supersymmetry and sl(2, R) internal symmetry by a systematic use of superfield techniques and of an sl(2, R) covariant formalism. We provide a definition of N=2 basic and equivariant cohomology, generalizing Dijkgraaf’s and Moore’s, and of N=2 connection. For a general manifold with a group action, we show that: (i) the N=2 basic cohomology is isomorphic to the tensor product of the ordinary N=1 basic cohomology and a universal sl(2, R) group theoretic factor; (ii) the affine spaces of N=2 and N=1 connections are isomorphic.