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| VOLUME 117 (2023) | ISSUE 8 | PAGE 632 |
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Gauge equivalence between 1 + 1 rational Calogero-Moser field theory and higher rank Landau-Lifshitz equation
K. Atalikov+*, A. Zotov+*× 1)
+Steklov Mathematical Institute of Russian Academy of Sciences, 119991 Moscow, Russia *National Research Center "Kurchatov Institute", 123182 Moscow, Russia ×National Research University Higher School of Economics, 119048 Moscow, Russia
Abstract
In this paper we study 1 + 1 field generalization of the rational N-body Calogero-Moser model. We show that this model is gauge equivalent to some special higher rank matrix Landau-Lifshitz equation. The latter equation is described in terms of GLN rational R-matrix, which turns into the 11-vertex R-matrix in the N=2 case. The rational R-matrix satisfies the associative Yang-Baxter equation, which underlies construction of the Lax pair for the Zakharov-Shabat equation. The field analogue of the IRF-Vertex transformation is proposed. It allows to compute explicit change of variables between the field Calogero-Moser model and the Landau-Lifshitz equation. |