On classical q-deformations of integrable σ-models

Abstract

A bstract A procedure is developed for constructing deformations of integrable σ -models which are themselves classically integrable. When applied to the principal chiral model on any compact Lie group F , one recovers the Yang-Baxter σ -model introduced a few years ago by C. Klimčík. In the case of the symmetric space σ -model on F/G we obtain a new one-parameter family of integrable σ -models. The actions of these models correspond to a deformation of the target space geometry and include a torsion term. An interesting feature of the construction is the q -deformation of the symmetry corresponding to left multiplication in the original models, which becomes replaced by a classical q -deformed Poisson-Hopf algebra. Another noteworthy aspect of the deformation in the coset σ -model case is that it interpolates between a compact and a non-compact symmetric space. This is exemplified in the case of the SU(2) / U(1) coset σ -model which interpolates all the way to the SU(1 , 1) / U(1) coset σ -model.