Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable sigma-model

TL;DR

This paper introduces a multi-parameter integrable deformation of the principal chiral model that unifies several known deformations, including Yang-Baxter, bi-Yang-Baxter, Wess-Zumino, and TsT transformations, and relates to the Lukyanov model for SU(2).

Contribution

The authors develop a comprehensive four-parameter integrable deformation framework that encompasses multiple known models and connects to the Lukyanov model for SU(2).

Findings

Unified multi-parameter deformation includes known models as special cases.

Demonstrated equivalence to Lukyanov model for SU(2).

Maintains integrability across the deformation parameters.

Abstract

A multi-parameter integrable deformation of the principal chiral model is presented. The Yang-Baxter and bi-Yang-Baxter sigma-models, the principal chiral model plus a Wess-Zumino term and the TsT transformation of the principal chiral model are all recovered when the appropriate deformation parameters vanish. When the Lie group is SU(2), we show that this four-parameter integrable deformation of the SU(2) principal chiral model corresponds to the Lukyanov model.