Field theory generalizations of two-body Calogero-Moser models in the form of Landau-Lifshitz equations

We give detailed description for continuous version of the classical IRF-Vertex relation, where on the IRF side we deal with the Calogero-Moser-Sutherland models. Our study is based on constructing modifications of the Higgs bundles of infinite rank over elliptic curve and its degenerations. In this way the previously predicted gauge equivalence between L-A pairs of the Landau-Lifshitz type equations and 1 + 1 field theory generalization of the Calogero-Moser-Sutherland models is described. In this paper the sl(2) case is studied. Explicit changes of variables are obtained between the rational, trigonometric and elliptic models. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper discusses the continuous version of the classical IRF-Vertex relation in the context of the Calogero-Moser-Sutherland models. The study is based on constructing modifications of infinite rank Higgs bundles over elliptic curves and their degenerations, and describes the previously predicted gauge equivalence between L-A pairs of Landau-Lifshitz type equations and 1 + 1 field theory generalization of the Calogero-Moser-Sutherland models. The sl(2) case is specifically studied, with explicit changes of variables obtained between rational, trigonometric, and elliptic models.