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A large class of integrable deformations of the Principal Chiral Model, knownas the Yang-Baxter deformations, are governed by skew-symmetric R-matricessolving the (modified) classical Yang-Baxter equation. We carry out asystematic investigation of these deformations in the presence of theWess-Zumino term for simple Lie groups, working in a framework that treats bothinhomogeneous and homogeneous deformations on the same footing. After analysingthe cohomological conditions under which such a deformation is admissible, weconsider an action for the general Yang-Baxter deformation of the PrincipalChiral Model plus Wess-Zumino term and prove its classical integrability. Wealso show how the model is found from a number of alternative formulations:affine Gaudin models, E-models, 4-dimensional Chern-Simons theory and, forhomogeneous deformations, non-abelian T-duality.

Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term