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Integrable Systems of Finite Type from F-Cohomological Field Theories Without Unit

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Abstract

One of many manifestations of a deep relation between the topology of the moduli spaces of algebraic curves and the theory of integrable systems is a recent construction of Arsie, Lorenzoni, Rossi, and the first author associating an integrable system of evolutionary PDEs to an F-cohomological field theory (F-CohFT), which is a collection of cohomology classes on the moduli spaces of curves satisfying certain natural splitting properties. Typically, these PDEs have an infinite expansion in the dispersive parameter, which happens because they involve contributions from the moduli spaces of curves of arbitrarily large genus. In this paper, for each rank \(N\ge 2\), we present a family of F-CohFTs without unit, for which the equations of the associated integrable system have a finite expansion in the dispersive parameter. For \(N=2\), we explicitly compute the primary flows of this integrable system.

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Acknowledgements

The work of A. B. is supported by the Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1675 with the Ministry of Science and Higher Education of the Russian Federation. A.B. is grateful to A. Mikhailov, P. Rossi, and V. Sokolov for motivating discussions about the finiteness of the integrable systems associated to F-CohFTs.

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Authors and Affiliations

  1. Faculty of Mathematics, National Research University Higher School of Economics, 6 Usacheva str., Moscow, Russian Federation, 119048

    Alexandr Buryak & Danil Gubarevich

  2. Center for Advanced Studies, Skolkovo Institute of Science and Technology, 1 Nobel str., Moscow, Russian Federation, 143026

    Alexandr Buryak

  3. Novosibirsk State University, 1 Pirogova str., Novosibirsk, 630090, Russian Federation

    Alexandr Buryak

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  1. Alexandr Buryak
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  2. Danil Gubarevich
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Correspondence to Alexandr Buryak.

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Communicated by Michael Gekhtman.

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Buryak, A., Gubarevich, D. Integrable Systems of Finite Type from F-Cohomological Field Theories Without Unit. Math Phys Anal Geom 26, 23 (2023). https://doi.org/10.1007/s11040-023-09463-8

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