Gauge Conditions for the Constrained-WZNW--Toda Reductions

TL;DR

This paper explores gauge conditions in constrained-WZNW--Toda theories for simple Lie algebras, unifying different approaches and explicitly deriving solutions, with implications for affine Toda theories.

Contribution

It unifies various gauge approaches to constrained-WZNW--Toda systems and explicitly determines solution expansions, extending results to semi-integral gradations and affine Toda theories.

Findings

Unified formulae for gauge transformations in WZNW--Toda theories.

Explicit holomorphic expansion of solutions for reduced WZNW models.

Applicability of results to affine Toda theories.

Abstract

There is a constrained-WZNW--Toda theory for any simple Lie algebra equipped with an integral gradation. It is explained how the different approaches to these dynamical systems are related by gauge transformations. Combining Gauss decompositions in relevent gauges, we unify formulae already derived, and explictly determine the holomorphic expansion of the conformally reduced WZNW solutions - whose restriction gives the solutions of the Toda equations. The same takes place also for semi-integral gradations. Most of our conclusions are also applicable to the affine Toda theories.