Gauge equivalence of 1+1 Calogero-Moser-Sutherland field theory and higher rank trigonometric Landau-Lifshitz model
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929426787205120 |
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| author | Atalikov, K. Zotov, A. |
| author_facet | Atalikov, K. Zotov, A. |
| contents | We consider the classical integrable 1+1 trigonometric ${\rm gl}_N$ Landau-Lifshitz models constructed by means of quantum $R$-matrices satisfying also the associative Yang-Baxter equation. It is shown that 1+1 field analogue of the trigonometric Calogero-Moser-Sutherland model is gauge equivalent to the Landau-Lifshitz model, which arises from the Antonov-Hasegawa-Zabrodin trigonometric non-standard $R$-matrix. The latter generalizes the Cherednik's 7-vertex $R$-matrix in ${\rm GL}_2$ case to the case of ${\rm GL}_N$. Explicit change of variables between the 1+1 models is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00428 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gauge equivalence of 1+1 Calogero-Moser-Sutherland field theory and higher rank trigonometric Landau-Lifshitz model Atalikov, K. Zotov, A. High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems We consider the classical integrable 1+1 trigonometric ${\rm gl}_N$ Landau-Lifshitz models constructed by means of quantum $R$-matrices satisfying also the associative Yang-Baxter equation. It is shown that 1+1 field analogue of the trigonometric Calogero-Moser-Sutherland model is gauge equivalent to the Landau-Lifshitz model, which arises from the Antonov-Hasegawa-Zabrodin trigonometric non-standard $R$-matrix. The latter generalizes the Cherednik's 7-vertex $R$-matrix in ${\rm GL}_2$ case to the case of ${\rm GL}_N$. Explicit change of variables between the 1+1 models is obtained. |
| title | Gauge equivalence of 1+1 Calogero-Moser-Sutherland field theory and higher rank trigonometric Landau-Lifshitz model |
| topic | High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2403.00428 |