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

TL;DR

This paper systematically studies integrable Yang-Baxter deformations of the Principal Chiral Model with Wess-Zumino term, establishing their classical integrability and connections to various formulations.

Contribution

It provides a unified framework for Yang-Baxter deformations with Wess-Zumino term, analyzing cohomological conditions and demonstrating integrability.

Findings

Classical integrability of the deformed models is proven.

Connections to affine Gaudin models, E-models, and 4D Chern-Simons are established.

Conditions for admissibility of deformations are characterized.

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, E-models, 4-dimensional Chern-Simons theory and, for homogeneous deformations, non-abelian T-duality.