The Global Phase Space Structure of the Wess-Zumino-Witten Model

TL;DR

This paper characterizes the phase space of the Wess-Zumino-Witten model on a cylinder with a compact Lie group target, revealing its structure as the cotangent bundle of the loop group and deriving its Poisson brackets.

Contribution

It introduces a new parametrization of the solution space and demonstrates the phase space as the cotangent bundle of the loop group, unifying different formulations.

Findings

Phase space is the cotangent bundle of the loop group G.

Poisson brackets in this phase space are explicitly derived.

Different formulations are shown as gauge fixings within this framework.

Abstract

We present a new parametrisation of the space of solutions of the Wess-Zumino-Witten model on a cylinder, with target space a compact, connected Lie group G. Using the covariant canonical approach the phase space of the theory is shown to be the co-tangent bundle of the loop group of the Lie group G, in agreement with the result from the Hamiltonian approach. The Poisson brackets in this phase space are derived. Other formulations in the literature are shown to be obtained by locally-valid gauge-fixings in this phase space.