Integrable deformations of principal chiral model from solutions of associative Yang-Baxter equation
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915785360801792 |
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| author | Domanevsky, D. Levin, A. Olshanetsky, M. Zotov, A. |
| author_facet | Domanevsky, D. Levin, A. Olshanetsky, M. Zotov, A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08777 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integrable deformations of principal chiral model from solutions of associative Yang-Baxter equation Domanevsky, D. Levin, A. Olshanetsky, M. Zotov, A. Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems 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. |
| title | Integrable deformations of principal chiral model from solutions of associative Yang-Baxter equation |
| topic | Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2501.08777 |