Integrable deformations of principal chiral model from solutions of associative Yang-Baxter equation

TL;DR

This paper explores new integrable deformations of classical principal chiral and Gaudin models using solutions to the associative Yang-Baxter equation, linking algebraic structures to integrability.

Contribution

It introduces a novel class of deformations generated by R-matrices satisfying the associative Yang-Baxter equation, expanding the understanding of integrable models.

Findings

Derived equations of motion from R-matrix coefficients

Identified deformation via twist function as cocentral charge

Connected deformations to Hitchin's integrable systems

Abstract

We describe deformations of the classical principle chiral model and 1+1 Gaudin model related to ${\rm GL}_N$ Lie group. The deformations are generated by $R$-matrices satisfying the associative Yang-Baxter equation. Using the coefficients of the expansion for these $R$-matrices we derive equations of motion based on a certain ansatz for $U$-$V$ pair satisfying the Zakharov-Shabat equation. Another deformation comes from the twist function, which we identify with the cocentral charge in the affine Higgs bundle underlying the Hitchin approach to 2d integrable models.