G/G Models and W_N strings

TL;DR

This paper computes the BRST cohomology of the G/G topological model for A^{(1)}_{N-1} and shows its relation to (p,q) W_N minimal models coupled to W_N gravity at specific levels.

Contribution

It derives the BRST cohomology for the G/G model in the A^{(1)}_{N-1} case and links it to (p,q) W_N minimal models coupled to W_N gravity.

Findings

BRST cohomology explicitly derived for A^{(1)}_{N-1}

Shows correspondence with (p,q) W_N minimal models

Identifies additional topological sectors

Abstract

We derive the BRST cohomology of the G/G topological model for the case of A^{(1)}_{N-1} . It is shown that at level k={p/q}-N the latter describes the (p,q) W_N minimal model coupled to $W_N$ gravity (plus some extra ``topological sectors").