Construction of BRST invariant states in GH WZNW models

We study the cohomology arising in the BRST formulation of GH gauged WZNW models. We will derive for a general simple group H with arbitrary representations and levels, 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 ±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.