The WZW Model as a Dynamical System on Affine Lie Groups

TL;DR

This paper introduces new formulations of the WZW model directly on affine Lie groups, revealing novel mechanical and field theory perspectives and establishing a translation dictionary to connect these formulations with traditional models.

Contribution

It presents multiple new formulations of the WZW model on affine Lie groups, including one-dimensional mechanical and three-dimensional field theory versions, and develops a translation dictionary linking these to conventional models.

Findings

New formulations of WZW on affine Lie groups as mechanical and field theories

Established a translation dictionary connecting affine formulations to traditional models

Expressed WZW as a three-dimensional field theory with a four-dimensional WZW term

Abstract

Working directly on affine Lie groups, we construct several new formulations of the WZW model. In one formulation WZW is expressed as a one-dimensional mechanical system whose variables are coordinates on the affine Lie group. When written in terms of the affine group element, this formulation exhibits a two-dimensional WZW term. In another formulation WZW is written as a two-dimensional field theory, with a three-dimensional WZW term, whose fields are coordinates on the affine group. On the basis of these equivalent formulations, we develop a translation dictionary in which the new formulations on the affine Lie group are understood as mode formulations of the conventional WZW formulation on the Lie group. Using this dictionary, we also express WZW as a three-dimensional field theory on the Lie group with a four-dimensional WZW term.