Semi-infinite cohomology of W-algebras

TL;DR

This paper extends homological methods to W-algebras, specifically computing semi-infinite cohomology of the W_3 algebra, with applications to physics such as W_3 gravity and minimal models.

Contribution

It introduces generalized homological techniques for W-algebras and computes semi-infinite cohomology for the W_3 algebra on various modules.

Findings

Computed semi-infinite cohomology of W_3 algebra

Identified physical states in W_3 gravity models

Connected cohomology results to minimal models and free scalar fields

Abstract

We generalize some of the standard homological techniques to $\cW$-algebras, and compute the semi-infinite cohomology of the $\cW_3$ algebra on a variety of modules. These computations provide physical states in $\cW_3$ gravity coupled to $\cW_3$ minimal models and to two free scalar fields.