2022/12/07 by Thomas W. Grimm, Grimm, Thomas W., Jeroen Monnee +1
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2212.03893
openalex publication_date 2022/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.