The quantum tropical vertex

IF 2 1区 数学 Geometry & Topology Pub Date : 2018-06-29 DOI:10.2140/gt.2020.24.1297
Pierrick Bousseau
{"title":"The quantum tropical vertex","authors":"Pierrick Bousseau","doi":"10.2140/gt.2020.24.1297","DOIUrl":null,"url":null,"abstract":"Gross-Pandharipande-Siebert have shown that the 2-dimensional Kontsevich-Soibelman scattering diagrams compute certain genus zero log Gromov-Witten invariants of log Calabi-Yau surfaces. We show that the $q$-refined 2-dimensional Kontsevich-Soibelman scattering diagrams compute, after the change of variables $q=e^{i \\hbar}$, generating series of certain higher genus log Gromov-Witten invariants of log Calabi-Yau surfaces. \nThis result provides a mathematically rigorous realization of the physical derivation of the refined wall-crossing formula from topological string theory proposed by Cecotti-Vafa, and in particular can be seen as a non-trivial mathematical check of the connection suggested by Witten between higher genus open A-model and Chern-Simons theory. \nWe also prove some new BPS integrality results and propose some other BPS integrality conjectures.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"11 1","pages":""},"PeriodicalIF":2.0000,"publicationDate":"2018-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"45","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geometry & Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/gt.2020.24.1297","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 45

Abstract

Gross-Pandharipande-Siebert have shown that the 2-dimensional Kontsevich-Soibelman scattering diagrams compute certain genus zero log Gromov-Witten invariants of log Calabi-Yau surfaces. We show that the $q$-refined 2-dimensional Kontsevich-Soibelman scattering diagrams compute, after the change of variables $q=e^{i \hbar}$, generating series of certain higher genus log Gromov-Witten invariants of log Calabi-Yau surfaces. This result provides a mathematically rigorous realization of the physical derivation of the refined wall-crossing formula from topological string theory proposed by Cecotti-Vafa, and in particular can be seen as a non-trivial mathematical check of the connection suggested by Witten between higher genus open A-model and Chern-Simons theory. We also prove some new BPS integrality results and propose some other BPS integrality conjectures.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
量子热带顶点
Gross-Pandharipande-Siebert证明了二维kontsevic - soibelman散射图计算了对数Calabi-Yau曲面的某些格零对数Gromov-Witten不变量。我们证明了$q$精化的二维kontsevic - soibelman散射图在变量$q=e^{i \hbar}$改变后,可以计算出log Calabi-Yau曲面的若干高属log gromovo - witten不变量序列。这一结果为从Cecotti-Vafa提出的拓扑弦理论推导出的精细化过壁公式的物理推导提供了数学上的严格实现,尤其可以看作是对Witten提出的高属开a模型与chen - simons理论之间联系的非平凡数学检验。我们还证明了一些新的BPS完整性结果,并提出了其他一些关于BPS完整性的猜想。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Geometry & Topology
Geometry & Topology 数学-数学
自引率
5.00%
发文量
34
期刊介绍: Geometry and Topology is a fully refereed journal covering all of geometry and topology, broadly understood. G&T is published in electronic and print formats by Mathematical Sciences Publishers. The purpose of Geometry & Topology is the advancement of mathematics. Editors evaluate submitted papers strictly on the basis of scientific merit, without regard to authors" nationality, country of residence, institutional affiliation, sex, ethnic origin, or political views.
期刊最新文献
Rational Pontryagin classes of Euclidean fiber bundles An Introduction to Boundedly Controlled Simple Homotopy Theory Gauge Theory and Smooth Structures on 4-Manifolds Isolated Critical Points of Maps from R4 to R2 and a Natural Splitting of the Milnor Number of a Classical Fibred Link, Part II Equivariant Handles in Finite Group Actions
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1