Bi-Yang-Baxter Models and Sl(2)-orbits

TL;DR

This paper introduces new classical solutions to bi-Yang-Baxter models for general groups, linking integrable sigma-models with Hodge theory through the use of Sl(2)-orbits.

Contribution

It presents a novel class of solutions for bi-Yang-Baxter models and establishes a connection between integrable models and asymptotic Hodge theory.

Findings

Solutions for SL(2,R) model mapped to SU(2) solutions

Construction of solutions from Sl(2)-orbits

Evidence of relation between sigma-models and Hodge theory

Abstract

We study integrable deformations of two-dimensional non-linear sigma-models and present a new class of classical solutions to critical bi-Yang-Baxter models for general groups. For the simplest example, namely the SL(2,R) bi-Yang-Baxter model, we show that our solutions can be mapped to the known complex uniton solutions of the SU(2) bi-Yang-Baxter model. In general, our solutions are constructed from so-called Sl(2)-orbits that play a central role in the study of asymptotic Hodge theory. This provides further evidence for a close relation between integrable non-linear sigma-models and the mathematical principles underlying Hodge theory. We have also included a basic introduction to the relevant aspects of asymptotic Hodge theory and have provided some simple examples.