The Canonical Structure of Wess-Zumino-Witten Models

TL;DR

This paper thoroughly analyzes the phase space and symplectic structure of Wess-Zumino-Witten models on a circle, including supersymmetric and gauged variants, providing detailed derivations of their Poisson brackets.

Contribution

It offers a detailed derivation of the Poisson brackets and canonical structure for Wess-Zumino-Witten models, including supersymmetric and gauged versions, clarifying their phase space geometry.

Findings

Explicit symplectic form for the WZW model on a circle

Derivation of Poisson brackets for the model

Analysis of canonical structure in supersymmetric and gauged cases

Abstract

The phase space of the Wess-Zumino-Witten model on a circle with target space a compact, connected, semisimple Lie group $G$ is defined and the corresponding symplectic form is given. We present a careful derivation of the Poisson brackets of the Wess-Zumino-Witten model. We also study the canonical structure of the supersymmetric and the gauged Wess-Zumino-Witten models.