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Abstract <p> We review the construction of classical elliptic integrable systems on the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathrm{SL}(N,\mathbb C)\)</EquationSource> </InlineEquation> Higgs bundles with non-trivial characteristic classes. The set of integrable models includes the Calogero–Moser system, its spin generalization, the Euler–Arnold top, and the Gaudin models. In some particular cases, mixed-type models known as the generalized models of interacting tops appear. Then we also review the field generalizations for these models on the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\((1\,{+}\,1)\)</EquationSource> </InlineEquation>-dimensional space–time. Finally, we propose a Maillet-type classical <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(r\)</EquationSource> </InlineEquation>-matrix structure for the field analog of the generalized model of interacting tops corresponding to <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathrm{SL}\)</EquationSource> </InlineEquation>-bundles with non-trivial characteristic classes. </p>

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2D Classical Integrable Field Theories from Hitchin Systems on \(\mathrm{SL}(NM,\mathbb C)\)-Bundles with Non-trivial Characteristic Classes

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Andrei Zotov

摘要

Abstract

We review the construction of classical elliptic integrable systems on the \(\mathrm{SL}(N,\mathbb C)\) Higgs bundles with non-trivial characteristic classes. The set of integrable models includes the Calogero–Moser system, its spin generalization, the Euler–Arnold top, and the Gaudin models. In some particular cases, mixed-type models known as the generalized models of interacting tops appear. Then we also review the field generalizations for these models on the \((1\,{+}\,1)\) -dimensional space–time. Finally, we propose a Maillet-type classical \(r\) -matrix structure for the field analog of the generalized model of interacting tops corresponding to \(\mathrm{SL}\) -bundles with non-trivial characteristic classes.