Extended Non-Abelian Gauge Symmetries in Classical WZNW Model

TL;DR

This paper explores higher spin extensions of nonabelian gauge symmetries in the classical WZNW model, revealing linear and nonlinear realizations of extended affine Kac-Moody algebras and their properties.

Contribution

It introduces both linear and nonlinear realizations of higher spin extended affine Kac-Moody algebras within the classical WZNW model, highlighting their properties and limitations.

Findings

Higher spin currents do not form an invariant space under their transformations.

The model admits equivalent linear and nonlinear realizations of the extended algebra.

Higher spin gauge symmetries cannot be gauged due to non-invariance.

Abstract

The present paper is revised copy of hep-th/9303087 in which higher spin extensions of the nonabelian gauge symmetries for the classical WZNW model are considered. Both linear and nonlinear realizations of the extended affine Kac-Moody algebra are obtained. A characteristic property of the WZNW model is that it admits a higher spin linear realization of the extended affine Kac-Moody algebra which is equivalent to the corresponding higher spin nonlinear realization of the same algebra. However, in both cases the higher spin currents do not form an invariant space with respect to their generating transformations. This makes it imposible for this symmetry to be gauged.