Abstract
We study integrable deformations of two-dimensional non-linear σ-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 σ-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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Acknowledgments
We would like to thank Falk Hassler, Damian van de Heisteeg, Dirk Schuricht, Daniel Thompson and Mick van Vliet for useful discussions and comments. This research is supported, in part, by the Dutch Research Council (NWO) via a Start-Up grant and a Vici grant.
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Grimm, T.W., Monnee, J. Bi-Yang-Baxter models and Sl(2)-orbits. J. High Energ. Phys. 2023, 123 (2023). https://doi.org/10.1007/JHEP11(2023)123
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DOI: https://doi.org/10.1007/JHEP11(2023)123