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

TL;DR

This paper explores the quantum gauge group structure of the 2D SU(n) WZNW model, revealing how physical states maintain monodromy invariance through invariance under a permuted coproduct of quantum groups.

Contribution

It introduces a gauge-theoretic approach to understanding the quantum gauge group structure and monodromy invariance in the 2D SU(n) WZNW model.

Findings

Physical states are invariant under the permuted coproduct of quantum groups.

The analysis provides a complete description of constraints for n=2.

Exchange relations differ for Gauss components of monodromy matrices.

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.