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arXiv · 2212.03893

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

Thomas W. Grimm·Jeroen Monnee
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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.

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Thomas W. Grimm, Jeroen Monnee. 2022-12-07. Bi-Yang-Baxter Models and Sl(2)-orbits. https://arxiv.org/abs/2212.03893

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