A Finite Dimensional Gauge Problem in the WZNW Model

Abstract

The left and right zero modes of the level k SU(n) WZNW model give rise to a pair of isomorphic (left and right) mutually commuting quantum matrix algebras. For a deformation parameter q being an even (2h-th, h = k + n) root of unity each of these matrix algebras admits an ideal such that the corresponding factor algebra is finite dimensional. The structure of superselection sectors of the (diagonal) 2D WZNW model is then reduced to a finite dimensional problem of a gauge theory type. For n=2 this problem is solved using a generalized BRS formalism.

20 pages, LATEX. Talk presented by I.T. Todorov at the International symposium "Quantum Theory and Symmetries"' 18-22 July 1999, Goslar, Germany

References in corpus (7)

• Operads and Motives in Deformation Quantization
• A Quasi-Hopf algebra interpretation of quantum 3-j and 6-j symbols and difference equations
• Lattice Wess-Zumino-Witten Model and Quantum Groups
• Universal $q$-differential calculus and $q$-analog of homological algebra
• Chiral Extensions of the WZNW Phase Space, Poisson-Lie Symmetries and Groupoids
• Quantisation of the SU(N) WZW Model at Level $k$
• Representation Theory of Lattice Current Algebras

Cited by in corpus (5)

• Zero modes' fusion ring and braid group representations for the extended chiral su(2) WZNW model
• Chiral zero modes of the SU(n) Wess-Zumino-Novikov-Witten model
• Regular basis and R-matrices for the su(n)_k Knizhnik-Zamolodchikov equation
• Canonical approach to the WZNW model
• Generalized Grassmann Algebras and its Connection to the Extended Supersymmetric Models