The Semi-Infinite Cohomology of Affine Lie Algebras (original) (raw)

We study the semi-infinite or BRST cohomology of affine Lie algebras in detail. This cohomology is relevant in the BRST approach to gauged WZNW models. Our main result is to prove necessary and sufficient conditions on ghost numbers and weights for non-trivial elements in the cohomology. In particular we prove the existence of an infinite sequence of elements in the cohomology for non-zero ghost numbers. This will imply that the BRST approach to topological WZNW model admits many more states than a conventional coset construction. This conclusion also applies to some non-topological models.