Current Algebra of WZNW Models at and away from Criticality

TL;DR

This paper derives the current algebra for WZNW models, showing how it interpolates between the conformal WZW algebra and the algebra of the ordinary chiral model as the coupling varies.

Contribution

It explicitly constructs the current algebra deformation from the WZW model to the chiral model using the coupling constant as a deformation parameter.

Findings

At critical coupling, the algebra reduces to two commuting Kac-Moody algebras.

In the zero coupling limit, it recovers the current algebra of the chiral model.

The deformation provides a continuous interpolation between the two models.

Abstract

We derive the current algebra of principal chiral models with a Wess-Zumino term. At the critical coupling where the model becomes conformally invariant (Wess-Zumino-Novikov-Witten theory), this algebra reduces to two commuting Kac-Moody algebras, while in the limit where the coupling constant is taken to zero (ordinary chiral model), we recover the current algebra of that model. In this way, the latter is explicitly realized as a deformation of the former, with the coupling constant as the deformation parameter.