Classical Integrability of Non Abelian Affine Toda Models

TL;DR

This paper constructs non-abelian affine Toda models using gauged WZW models, demonstrating their classical integrability through zero curvature representation and classical r-matrix, and exploring soliton solutions with complex charges.

Contribution

It introduces a new class of non-abelian affine Toda models and proves their classical integrability with explicit constructions.

Findings

Existence of soliton solutions with electric and topological charges.

Construction of zero curvature representation for these models.

Derivation of the classical r-matrix confirming integrability.

Abstract

A class of non abelian affine Toda models is constructed in terms of the axial and vector gauged WZW model. It is shown that the multivacua structure of the potential together with non abelian nature of the zero grade subalgebra allows soliton solutions with non trivial electric and topological charges. Their zero curvature representation and the classical $r$-matrix are also constructed in order to prove their classical integrability.