On the W-gravity spectrum and its G-structure

TL;DR

This paper investigates the BRST cohomology of $fg$-related models coupled to $fg$ gravity, revealing complex relations to twisted Fock modules and advancing understanding of $fg$-gravity spectra.

Contribution

It provides new results on the BRST cohomology of $fg$ minimal models and scalar fields coupled to $fg$ gravity, highlighting intricate algebraic structures.

Findings

BRST cohomology results for $fg$ minimal models coupled to $fg$ gravity

Analysis of scalar fields coupled to $fg$ gravity

Discovery of relations to twisted $fg$ cohomology and Fock modules

Abstract

We present results for the BRST cohomology of $\cW[\bfg]$ minimal models coupled to $\cW[\bfg]$ gravity, as well as scalar fields coupled to $\cW[\bfg]$ gravity. In the latter case we explore an intricate relation to the (twisted) $\bfg$ cohomology of a product of two twisted Fock modules.