GRAVITATIONAL DRESSING OF MASSIVE SOLITON THEORIES

The massive soliton theories describe integrable perturbations of WZW cosets as generalized multi-component sine-Gordon models. We study the ir coupling to 2-dim gravity in the conformal gauge and show that the resulting models can be interpreted as conformal non-Abelian Toda theo ries when a certain algebraic condition is satisfied. These models, ho wever, do not provide quantum mechanically consistent string backgroun ds in the case the underlying WZW constraints are first solved classic ally.