{"title":"Topological 1D gravity, KP hierarchy, and orbifold Euler characteristics of M‾g,n","authors":"Zhiyuan Wang , Jian Zhou","doi":"10.1016/j.nuclphysb.2025.116822","DOIUrl":null,"url":null,"abstract":"<div><div>In this work we study the tau-function <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mn>1</mn><mi>D</mi></mrow></msup></math></span> of the KP hierarchy specified by the topological 1D gravity. As an application, we present two types of algorithms to compute the orbifold Euler characteristics of the moduli spaces <span><math><msub><mrow><mover><mrow><mi>M</mi></mrow><mo>‾</mo></mover></mrow><mrow><mi>g</mi><mo>,</mo><mi>n</mi></mrow></msub></math></span> of stable curves. The first is to use (fat or thin) topological recursion formulas emerging from the Virasoro constraints for <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mn>1</mn><mi>D</mi></mrow></msup></math></span>; and the second is to use a formula for the connected <em>n</em>-point functions of a KP tau-function in terms of its affine coordinates on the Sato Grassmannian. This is a sequel to an earlier work <span><span>[34]</span></span>.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1012 ","pages":"Article 116822"},"PeriodicalIF":2.5000,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nuclear Physics B","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S055032132500032X","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, PARTICLES & FIELDS","Score":null,"Total":0}
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Abstract
In this work we study the tau-function of the KP hierarchy specified by the topological 1D gravity. As an application, we present two types of algorithms to compute the orbifold Euler characteristics of the moduli spaces of stable curves. The first is to use (fat or thin) topological recursion formulas emerging from the Virasoro constraints for ; and the second is to use a formula for the connected n-point functions of a KP tau-function in terms of its affine coordinates on the Sato Grassmannian. This is a sequel to an earlier work [34].
期刊介绍：
Nuclear Physics B focuses on the domain of high energy physics, quantum field theory, statistical systems, and mathematical physics, and includes four main sections: high energy physics - phenomenology, high energy physics - theory, high energy physics - experiment, and quantum field theory, statistical systems, and mathematical physics. The emphasis is on original research papers (Frontiers Articles or Full Length Articles), but Review Articles are also welcome.
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