The BRST formulation of G/H WZNW models

TL;DR

This paper develops a BRST-based formulation for G/H coset WZNW models, establishing its equivalence to traditional methods, and explores implications for representations, string theories, and partition functions.

Contribution

It introduces a BRST approach to G/H WZNW models, proving its equivalence to conventional formulations and connecting integrable and non-integrable representations.

Findings

Established the equivalence between BRST and conventional coset formulations.

Connected non-integrable representations to string theories with non-compact WZNW models.

Reproduced known results for specific G/H models using the BRST approach.

Abstract

We consider a BRST approach to G/H coset WZNW models, {\it i.e.} a formulation in which the coset is defined by a BRST condition. We will give the precise ingrediences needed for this formulation. Then we will prove the equivalence of this approach to the conventional coset formulation by solving the the BRST cohomology. This will reveal a remarkable connection between integrable representations and a class of non-integrable representations for negative levels. The latter representations are also connected to string theories based on non-compact WZNW models. The partition functions of G/H cosets are also considered. The BRST approach enables a covariant construction of these, which does not rely on the decomposition of G as $G/H\times H$. We show that for the well-studied examples of $SU(2)_k \times SU(2)_1/SU(2)_{k+1}$ and $SU(2)_k/U(1)$, we exactly reproduce the previously known results.