Alternative Canonical Formalism for the Wess-Zumino-Witten Model

TL;DR

This paper introduces a novel canonical quantization approach for the Wess-Zumino-Witten model involving two parameters, connecting it to generalized Thirring models and exploring non-compact affine Lie algebra structures.

Contribution

It presents a two-parameter canonical formalism for the WZW model, extending the usual single-parameter approach and linking it to generalized Thirring models and non-compact current algebras.

Findings

Two-parameter quantization relates to generalized Thirring models

Classical model admits non-compact affine Lie algebra structure

Existence of non-unitary quantizations with partial conformal invariance

Abstract

We study a canonical quantization of the Wess--Zumino--Witten (WZW) model which depends on two integer parameters rather than one. The usual theory can be obtained as a contraction, in which our two parameters go to infinity keeping the difference fixed. The quantum theory is equivalent to a generalized Thirring model, with left and right handed fermions transforming under different representations of the symmetry group. We also point out that the classical WZW model with a compact target space has a canonical formalism in which the current algebra is an affine Lie algebra of non--compact type. Also, there are some non--unitary quantizations of the WZW model in which there is invariance only under half the conformal algebra (one copy of the Virasoro algebra).