Semi-infinite cohomology in conformal field theory and 2d gravity

TL;DR

This paper explores methods for calculating semi-infinite cohomology in two-dimensional conformal field theories, focusing on coset models and 2D gravity coupled to conformal matter, relevant for BRST quantization.

Contribution

It introduces techniques for computing semi-infinite cohomology in specific 2D field theories, advancing understanding of their BRST quantization.

Findings

Developed methods for semi-infinite cohomology calculation

Applied techniques to coset models and 2D gravity

Enhanced understanding of BRST quantization in these theories

Abstract

We discuss various techniques for computing the semi-infinite cohomology of highest weight modules which arise in the BRST quantization of two dimensional field theories. In particular, we concentrate on two such theories -- the $G/H$ coset models and $2d$ gravity coupled to $c\leq 1$ conformal matter. (to appear in the proceedings of the XXV Karpacz Winter School)