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

TL;DR

This paper explores the structure of N=2 Super Virasoro algebra representations, their relation to 2D gravity models, and the Hamiltonian reduction of BRST complexes, providing new insights into the algebraic and geometric aspects of superconformal theories.

Contribution

It introduces a Hamiltonian reduction framework for the BRST complex of sl(N)/sl(N) cosets, linking N=2 superconformal algebras with 2D gravity and W-gravity models.

Findings

Resolutions for N=2 SVir irreducible representations are obtained.

The correspondence between N=2 minimal models and 2D gravity coupled models is established.

Explicit case of sl(2) reduction leading to N=2 Super Virasoro algebra presentation.

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.