Lagrangian formulation of symmetric space sine-Gordon models

The symmetric space sine-Gordon models arise by conformal reduction of ordinary 2-dim σ-models, and they are integrable exhibiting a black-hole type metric in target space. We provide a Lagrangian formulation of these systems by considering a triplet of Lie groups F ⊃ G ⊃ H. We show that for every symmetric space FG, the generalized sine-Gordon models can be derived from the GH WZW action, plus a potential term that is algebraically specified. Thus, the symmetric space sine-Gordon models describe certain integrable perturbations of coset conformal field theories at the classical level. We also briefly discuss their vacuum structure, Bäcklund transformations, and soliton solutions.