A Quantum Gauge Group Approach to the 2D SU(n) WZNW Model

Abstract

The canonical quantization of the WZNW model provides a complete set of exchange relations in the enlarged chiral state spaces that include the Gauss components of the monodromy matrices. Regarded as new dynamical variables, the elements of the latter cannot be identified -- they satisfy different exchange relations. Accordingly, the two dimensional theory expressed in terms of the left and right movers' fields does not automatically respect monodromy invariance. Continuing our recent analysis of the problem by gauge theory methods we conclude that physical states (on which the two dimensional field acts as a single valued operator) are invariant under the (permuted) coproduct of the left and right $U_q(sl(n))$. They satisfy additional constraints fully described for n=2.

10 pages, LATEX (Proposition 4.2 corrected, one reference added)

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• Chiral zero modes of the SU(n) Wess-Zumino-Novikov-Witten model
• Classical Wakimoto Realizations of Chiral WZNW Bloch Waves
• Indecomposable U_q(sl_n) modules for q^h = -1 and BRS intertwiners
• Zero modes of the SU(2)_k Wess-Zumino-Novikov-Witten model in Euler angles parametrization