Action-Angle Variables in the Quantum Wess-Zumino-Witten Model

Abstract

Wess-Zumino-Witten model (WZWM) is the important example of 2d conformal field theories (CFT) [1] which now are very actual due to their role in the string theory and in 2d statistical mechanics. The widespread belief is that WZWM is the universal object in the so-called rational CFT. Namely, any such theory can be obtained from the WZWM or its modification [2]. Thus it is plauzible to have a description, which allows to calculate physical quohtities such as statsums, correlators and so on. In fact, it turns out that WZWM is equivalent to a free theory on the classical and the quantum level. In this talk, which is based on the work [3], WZWM is described in terms of the action-angle variables. WZWM as a CFT due the special structure of the stress-energy tensor has an infinite sequence of integrals of motion. In fact, it turns out that the situation here is much more simpler in compare with the generic case — the WZWM belongs to the so-called c-integrable systems in accordance with the F.Calodgero classification. It’s mean that a system can be integrated by an algebraic changing of variables. As it was demonstrated recently by A.Zamolodchikov some of CFT can be deformed in a such way that only a subset of integrals is destroyed and the deformed system also has an infinite set of integrals [4].