On integrability of the Yang-Baxter $\si$-model

TL;DR

This paper proves the integrability of the Yang-Baxter sigma-model, a Poisson-Lie deformation of the principal chiral model, and provides a transformation linking solutions of both models, facilitating solution generation.

Contribution

It establishes the integrability of the Yang-Baxter sigma-model and introduces an explicit map connecting its solutions to those of the principal chiral model, enabling solution transfer.

Findings

Proved the integrability of the Yang-Baxter sigma-model.

Constructed an explicit solution transformation map.

Enabled direct transfer of dressing procedures between models.

Abstract

We prove the integrability of the Yang-Baxter $\si$-model which is the Poisson-Lie deformation of the principal chiral model. We find also an explicit one-to-one map transforming every solution of the principal chiral model into a solution of the deformed model. With the help of this map, the standard procedure of the dressing of the principal chiral solutions can be directly transferred into the deformed Yang-Baxter context.