Operator realization of the SU(2) WZNW model

TL;DR

This paper constructs an operator formalism for the SU(2) WZNW model, clarifying the quantum group symmetry and monodromy invariance by expressing chiral fields through vertex operators and q-Bose operators.

Contribution

It provides a consistent operator realization of the SU(2) WZNW model, resolving previous open questions about monodromy invariance and quantum group symmetry in the continuum limit.

Findings

Chiral quantum fields expressed as sums of vertex and q-Bose operators

Reconciliation of monodromy invariance with exchange relations

Establishment of a consistent operator formalism in the continuum

Abstract

Decoupling the chiral dynamics in the canonical approach to the WZNW model requires an extended phase space that includes left and right monodromy variables. Earlier work on the subject, which traced back the quantum qroup symmetry of the model to the Lie-Poisson symmetry of the chiral symplectic form, left some open questions: - How to reconcile the monodromy invariance of the local 2D group valued field (i.e., equality of the left and right monodromies) with the fact that the latter obey different exchange relations? - What is the status of the quantum group symmetry in the 2D theory in which the chiral fields commute? - Is there a consistent operator formalism in the chiral and in the extended 2D theory in the continuum limit? We propose a constructive affirmative answer to these questions for G=SU(2) by presenting the chiral quantum fields as sums of chiral vertex operators and q-Bose creation and annihilation operators.