Construction of BRST invariant states in $G/H$ WZNW models.

TL;DR

This paper analyzes the BRST cohomology in G/H gauged WZNW models, identifying conditions for non-trivial states and constructing them explicitly using highest weight null-states and perturbations.

Contribution

It provides a general method to construct BRST invariant states in G/H WZNW models for arbitrary simple groups and levels, using highest weight null-states and perturbation techniques.

Findings

Conditions for non-trivial cohomology are derived.

States in cohomology are explicitly constructed.

Ghost number assignments are determined by representations.

Abstract

We study the cohomology arising in the BRST formulation of G/H gauged WZNW models, i.e. in which the states of the gauged theory are projected out from the ungauged one by means of a BRST condition. We will derive for a general simple group $H$ with arbitrary level, conditions for which the cohomology is non-trivial. We show, by introducing a small perturbation due to Jantzen, in the highest weights of the representations, how states in the cohomology, "singlet pairs", arise from unphysical states, "Kugo-Ojima quartets", as the perturbation is set to zero. This will enable us to identify and construct states in the cohomology. The ghost numbers that will occur are $\pm p$, with $p$ uniquely determined by the representations of the algebras involved. Our construction is given in terms of the current modes and relies on the explicit form of highest weight null-states given by Malikov, Feigen and Fuchs.