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

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2023-09-09 DOI:10.1007/s11040-023-09463-8

Alexandr Buryak, Danil Gubarevich

引用次数: 1

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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无单位F-同调场论中的有限型可积系统

最近Arsie, Lorenzoni, Rossi和第一作者将演化偏微分方程的可积系统与f -上同调场理论(F-CohFT)联系起来，该理论是曲线模空间上满足某些自然分裂性质的上同调类的集合，这是代数曲线模空间拓扑与可积系统理论之间深刻关系的众多表现之一。通常，这些偏微分方程在色散参数上具有无限展开，这是因为它们涉及到任意大的曲线的模空间的贡献。对于每阶\(N\ge 2\)，我们给出了一类无单位的f - cohft族，其相关可积系统的方程在色散参数上有有限展开式。对于\(N=2\)，我们明确地计算了这个可积系统的主要流。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.