K. R. Atalikov, A. V. Zotov, “Gauge equivalence of <nobr>$1+1$</nobr> Calogero–Moser–Sutherland field theory and a higher-rank trigonometric Landau–Lifshitz model”, TMF, 2024, Volume 219, Number 3,Pages <nobr>545

This article is cited in 2 papers

Gauge equivalence of $1+1$ Calogero–Moser–Sutherland field theory and a higher-rank trigonometric Landau–Lifshitz model

K. R. Atalikov^a, A. V. Zotov^abc

^a National Research Centre "Kurchatov Institute", Moscow, Russian
^b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
^c Institute for Theoretical and Mathematical Physics, Lomonosov Moscow State University, Moscow, Russia

Abstract: We consider the classical integrable $(1+1)$ trigonometric $gl_N$ Landau–Lifshitz models constructed by means of quantum $R$-matrices that also satisfy the associative Yang–Baxter equation. It is shown that a $(1+1)$ field analogue of the trigonometric Calogero–Moser–Sutherland model is gauge equivalent to the Landau–Lifshitz model that arises from the Antonov–Hasegawa–Zabrodin trigonometric nonstandard $R$-matrix. The latter generalizes Cherednik's $7$-vertex $R$-matrix in the $GL_2$ case to the case of $GL_N$. An explicit change of variables between the $(1+1)$ models is obtained.

Keywords: integrable systems, soliton equations, Calogero–Moser model, Landau–Lifshitz equation.

Received: 04.03.2024
Revised: 04.03.2024

DOI: 10.4213/tmf10716