Supersymmetric semi--infinite cohomology and $N = 2$ superconformal structures

Abstract

We study supersymmetric semi-infinite cohomology and its $N = 2$ superconformal structure via the BRST reduction of an $N = {\frac{3}{2}}$ superconformal structure on the super-affine vertex algebra associated to a super Manin pair arising from the Kazama--Suzuki $N = 2$ condition. Moreover, we realize super coset models in terms of relative supersymmetric semi-infinite cohomology.