Generalized Toda Theories from WZNW Reduction

TL;DR

This paper explores generalized Toda field theories derived from WZNW reduction, analyzing gauge fixing, ${ m W}$ algebra structures, and mappings to free fields, extending results to standard Toda models.

Contribution

It provides a detailed analysis of gauge choices and ${ m W}$ algebra realizations in generalized Toda theories, connecting them to free field representations.

Findings

Different gauge fixings lead to various ${ m W}$ algebra realizations.

The mapping between Toda fields and free fields is explicitly constructed.

Results are applicable to both generalized and ordinary Toda theories.

Abstract

We reconsider the, by Brink and Vasiliev, recently proposed generalized Toda field theories using the framework of WZNW$\rightarrow$Toda reduction. The reduced theory has a gauge symmetry which can be fixed in various ways. We discuss some different gauge choices. In particular we study the ${\cal W}$ algebra associated with the generalized model in some different realizations, corresponding to different gauge choices. We also investigate the mapping between the Toda field and a free field and show the relation between the ${\cal W}$ algebra generators expressed in terms of the two different fields. All results apply also to the case of ordinary Toda theories.