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

Abstract

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

References in corpus (2)

• Lattice Wess-Zumino-Witten Model and Quantum Groups
• On the q-analog of homological algebra