Canonical Quantization of Interacting WZW Theories

TL;DR

This paper applies canonical quantization to a class of conformally-invariant interacting WZW theories, deriving the Virasoro centre and comparing it to BRST results, thus advancing understanding of their algebraic structure.

Contribution

It provides a new canonical quantization approach to interacting WZW theories and derives a general formula for the Virasoro centre, relaxing Toda theory constraints.

Findings

Derived the Virasoro centre for these theories.

Compared canonical and BRST methods, clarifying their relationship.

Revealed the algebraic structure of non-integrable conformal theories.

Abstract

Using canonical quantization we find the Virasoro centre for a class of conformally-invariant interacting Wess-Zumino-Witten theories. The theories have a group structure similar to that of Toda theories (both abelian and non-abelian) but the usual Toda constraints on the coupling constants are relaxed and the theories are not necessarily integrable. The general formula for the Virasoro centre is compared to that derived by BRST methods in the Toda case, and helps to explain the structure of the latter.