Integrable Sigma-models and Drinfeld-Sokolov Hierarchies

TL;DR

This paper establishes a connection between local commuting charges in integrable sigma-models with classical Lie groups and the conserved quantities in Drinfeld-Sokolov hierarchies, extending to exceptional groups and symmetric spaces.

Contribution

It demonstrates how Drinfeld-Sokolov construction can be used to identify commuting charges in a broad class of sigma-models, linking them to affine Toda field theories.

Findings

Commuting charges in sigma-models relate to Drinfeld-Sokolov hierarchies.

Extension of integrability results to exceptional groups and symmetric spaces.

Establishment of a direct link between sigma-models and affine Toda theories.

Abstract

Local commuting charges in sigma-models with classical Lie groups as target manifolds are shown to be related to the conserved quantities appearing in the Drinfeld-Sokolov (generalized mKdV) hierarchies. Conversely, the Drinfeld-Sokolov construction can be used to deduce the existence of commuting charges in these and in wider classes of sigma-models, including those whose target manifolds are exceptional groups or symmetric spaces. This establishes a direct link between commuting quantities in integrable sigma-models and in affine Toda field theories.