Generalized Toda Theories from WZNW Reduction

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.