TY - JOUR

T1 - Integrable Systems of Finite Type from F-Cohomological Field Theories Without Unit

AU - Buryak, Alexandr

AU - Gubarevich, Danil

N1 - 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.

PY - 2023/9

Y1 - 2023/9

N2 - 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≥ 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.

AB - 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≥ 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.

KW - Algebraic curve

KW - Cohomological field theory

KW - Integrable system

KW - Moduli space

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85170388854&origin=inward&txGid=857bf014d0934c0749ff270502e65ed2

UR - https://www.mendeley.com/catalogue/6b7655ac-a017-334a-a655-94fbf0dd4af0/

U2 - 10.1007/s11040-023-09463-8

DO - 10.1007/s11040-023-09463-8

M3 - Article

VL - 26

JO - Mathematical Physics Analysis and Geometry

JF - Mathematical Physics Analysis and Geometry

SN - 1385-0172

IS - 3

M1 - 23

ER -