The classical Yang-Baxter equation and the associated Yangian symmetry of gauged WZW-type theories

TL;DR

This paper constructs integrable structures for a two-parameter deformation of the Principal chiral model, revealing Yangian symmetry and connecting WZW models with non-Abelian T-duality.

Contribution

It introduces a new integrable deformation of the Principal chiral model, including a detailed derivation of the Yangian algebra and Serre relations.

Findings

Constructed the Lax pair and monodromy matrix for the deformation.

Derived the Yangian algebra using two independent methods.

Provided a detailed proof of the Serre relations for Yangian symmetry.

Abstract

We construct the Lax-pair, the classical monodromy matrix and the corresponding solution of the Yang--Baxter equation, for a two-parameter deformation of the Principal chiral model for a simple group. This deformation includes as a one-parameter subset, a class of integrable gauged WZW-type theories interpolating between the WZW model and the non-Abelian T-dual of the principal chiral model. We derive in full detail the Yangian algebra using two independent methods: by computing the algebra of the non-local charges and alternatively through an expansion of the Maillet brackets for the monodromy matrix. As a byproduct, we also provide a detailed general proof of the Serre relations for the Yangian symmetry.