Generalized cohomologies and the physical subspace of the $SU(2)$ WZNW model

Dubois-Violette, Michel; Todorov, Ivan T.

Generalized cohomologies and the physical subspace of the $SU(2)$ WZNW model

Authors

Description

The zero modes of the monodromy extended SU(2) WZNW model give rise to a gauge theory with a finite dimensional state space. A generalized BRS operator $A$ such that $A^h=0 (h=k+2=3,4,...$ being the height of the current algebra representation) acts in a (2h-1)-dimensional indefinite metric space $H_I$ of quantum group invariant vectors. The generalized cohomologies $Ker A^n/ Im A^{h-n} (n=1,..., h-1)$ are 1-dimensional. Their direct sum spans the physical subquotient of $H_I$.
12 pages, Latex2e, available at http://qcd.th.u-psud.fr