Gravitational dressing of massive soliton theories

TL;DR

This paper explores how massive soliton theories, which are integrable models related to sine-Gordon models, behave when coupled to 2D gravity, revealing their connection to conformal Toda theories under specific conditions.

Contribution

It demonstrates that certain massive soliton theories coupled to 2D gravity can be interpreted as conformal non-Abelian Toda theories when specific algebraic conditions are met.

Findings

Models can be seen as conformal non-Abelian Toda theories under algebraic conditions.

Coupling to 2D gravity reveals their conformal structure.

Quantum consistency issues arise when WZW constraints are classically solved.

Abstract

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