Yang–Baxter deformations of the principal chiral model plus Wess–Zumino term

Abstract

A large class of integrable deformations of the principal chiral model, known as the Yang–Baxter deformations, are governed by skew-symmetric R-matrices solving the (modified) classical Yang–Baxter equation. We carry out a systematic investigation of these deformations in the presence of the Wess–Zumino term for simple Lie groups, working in a framework that treats both inhomogeneous and homogeneous deformations on the same footing. After analysing the cohomological conditions under which such a deformation is admissible, we consider an action for the general Yang–Baxter deformation of the principal chiral model plus Wess–Zumino term and prove its classical integrability. We also show how the model is found from a number of alternative formulations: affine Gaudin models, -models, four-dimensional Chern–Simons theory and, for homogeneous deformations, non-abelian T-duality.