The hamiltonian reduction of the BRST complex and N=2 SUSY

Abstract

We study the nonunitary representations of N=2 Super Virasoro algebra for the rational central charges c<3. The resolutions for the irreducible representations of N=2 SVir in terms of the "2-d gravity modules" are obtained and their characters are computed. The correspondence between the N=2 nonunitary "minimal" models and the Virasoro minimal models coupled to 2-d gravity is shown at the level of states. We also define the hamiltonian reduction of the BRST complex of sl(N)/sl(N) coset to the BRST complex of the W-gravity coupled to the W matter. The case of sl(2) is considered explicitly. It leads to the presentation of N=2 Super Virasoro algebra by the Lie algebra cohomology. Finally, we reveal the mechanism of the correspondence between sl(2)/sl(2)$ coset and 2-d gravity.