The semi-infinite cohomology of affine Lie algebras

Details The semi-infinite cohomology of affine Lie algebras The semi-infinite cohomology of affine Lie algebras

1997-08-19

arxiv.org/abs/hep-th/9708100v1

Commun.Math.Phys. 194 (1998) 591-611

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, Latex, no figures

Scientific paper

10.1007/s002200050370

We study in detail the semi-infinite or BRST cohomology of general affine Lie algebras. This cohomology is relevant in the BRST approach to gauged WZNW models. 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. Our work will also contain results on the structure of Verma modules over affine Lie algebras. In particular, we generalize the results of Verma and Bernstein-Gel'fand-Gel'fand,for finite dimensional Lie algebras, on the structure and multiplicities of Verma modules.

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