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. © 2000 Elsevier Science B.V.
Basic and equivariant cohomology in balanced topological field theory / Zucchini R.. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - STAMPA. - 35:4(2000), pp. 299-332. [10.1016/S0393-0440(99)00047-9]
Basic and equivariant cohomology in balanced topological field theory
Zucchini R.Primo
2000
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. © 2000 Elsevier Science B.V.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
