拓扑1D重力，KP层次结构，M - g，n的轨道欧拉特征

IF 2.5 3区物理与天体物理 Q2 PHYSICS, PARTICLES & FIELDS

Nuclear Physics B Pub Date : 2025-02-06 DOI:10.1016/j.nuclphysb.2025.116822

Zhiyuan Wang , Jian Zhou

{"title":"拓扑1D重力，KP层次结构，M - g，n的轨道欧拉特征","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":"{\"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}","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}

引用次数: 0

摘要

本文研究了由拓扑一维重力指定的KP层次的tau函数Z1D。作为一种应用，我们提出了两种算法来计算稳定曲线的M - g，n模空间的轨道欧拉特征。首先是使用Z1D的Virasoro约束中出现的（胖或瘦）拓扑递归公式；第二个是用一个公式来表示一个KP函数的连通n点函数在Sato Grassmannian上的仿射坐标。这是早期作品b[34]的续集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Topological 1D gravity, KP hierarchy, and orbifold Euler characteristics of M‾g,n

In this work we study the tau-function

Z^{1 D}

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

{\overline{M}}_{g, n}

of stable curves. The first is to use (fat or thin) topological recursion formulas emerging from the Virasoro constraints for

Z^{1 D}

; 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].

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Nuclear Physics B 物理-物理：粒子与场物理

CiteScore

5.50

自引率

7.10%

发文量

302

审稿时长

1 months

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.