The WZNW model as an integrable perturbation of the Witten conformal point

TL;DR

This paper demonstrates that the WZNW model can be viewed as a relevant sigma-model perturbation of the conformal WZNW theory at the Witten point, with the flow to a positive level model being integrable.

Contribution

It establishes the interpretation of the WZNW model as a sigma-model perturbation around the conformal point and proves the integrability of the flow for negative level k.

Findings

Flow from negative to positive level k is integrable.

Perturbed WZNW model flows to the conformal WZNW model at large |k|.

Existence of conserved currents satisfying the Lax equation confirms integrability.

Abstract

We show that the WZNW model with arbitrary $\sigma$-model coupling constant may be viewed as a $\sigma$-model perturbation of the WZNW theory around the Witten conformal point. In order for the $\sigma$-model perturbation to be relevant, the level $k$ of the underlying affine algebra has to be negative. We prove that in the large $|k|$ limit the perturbed WZNW system with negative $k$ flows to the conformal WZNW model with positive level. The flow appears to be integrable due to the existence of conserved currents satisfying the Lax equation. This fact is in a favorable agreement with the integrability of the WZNW model discovered by Polyakov and Wiegmann within the Bethe ansatz technique.