Basic and equivariant cohomology in balanced topological held theory

[摘要] 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 shaw 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 affme spaces of N = 2 and N = 1 connections are isomorphic. (C) 2000 Elsevier Science B.V. All rights reserved.

[发布日期] 2000-10-01

[关键词] topological field theory;cohomology