Hybrid classical integrable structure of squashed sigma models - a short summary

Abstract

We give a short summary of our recent works on the classical integrable\nstructure of two-dimensional non-linear sigma models defined on squashed\nthree-dimensional spheres. There are two descriptions to describe the classical\ndynamics, 1) the rational description and 2) the trigonometric description. It\nis possible to construct two different types of Lax pairs depending on the\ndescriptions, and the classical integrability is shown by computing classical\nr/s-matrices satisfying the extended Yang-Baxter equation in both descriptions.\nIn the former the system is described as an integrable system of rational type.\nOn the other hand, in the latter it is described as trigonometric type. There\nexists a non-local map between the two descriptions and those are equivalent.\nThis is a non-local generalization of the left-right duality in principal\nchiral models.\n