塞尔伯格积分和多森科-法捷耶夫积分的奇异性

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Annales Henri Poincaré Pub Date : 2024-01-03 DOI:10.1007/s00023-023-01402-1

Ethan Sussman

{"title":"塞尔伯格积分和多森科-法捷耶夫积分的奇异性","authors":"Ethan Sussman","doi":"10.1007/s00023-023-01402-1","DOIUrl":null,"url":null,"abstract":"<div><p>We discuss the meromorphic continuation of certain hypergeometric integrals modeled on the Selberg integral, including the 3-point and 4-point functions of BPZ’s minimal models of 2D CFT as described by Felder & Silvotti and Dotsenko & Fateev (the “Coulomb gas formalism”). This is accomplished via a geometric analysis of the singularities of the integrands. In the case that the integrand is symmetric (as in the Selberg integral itself) or, more generally, what we call “DF-symmetric,” we show that a number of apparent singularities are removable, as required for the construction of the minimal models via these methods.\n</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 9","pages":"3957 - 4032"},"PeriodicalIF":1.4000,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-023-01402-1.pdf","citationCount":"0","resultStr":"{\"title\":\"The Singularities of Selberg- and Dotsenko–Fateev-Like Integrals\",\"authors\":\"Ethan Sussman\",\"doi\":\"10.1007/s00023-023-01402-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We discuss the meromorphic continuation of certain hypergeometric integrals modeled on the Selberg integral, including the 3-point and 4-point functions of BPZ’s minimal models of 2D CFT as described by Felder & Silvotti and Dotsenko & Fateev (the “Coulomb gas formalism”). This is accomplished via a geometric analysis of the singularities of the integrands. In the case that the integrand is symmetric (as in the Selberg integral itself) or, more generally, what we call “DF-symmetric,” we show that a number of apparent singularities are removable, as required for the construction of the minimal models via these methods.\\n</p></div>\",\"PeriodicalId\":463,\"journal\":{\"name\":\"Annales Henri Poincaré\",\"volume\":\"25 9\",\"pages\":\"3957 - 4032\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-01-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00023-023-01402-1.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Henri Poincaré\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00023-023-01402-1\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Henri Poincaré","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1007/s00023-023-01402-1","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 0

摘要

摘要我们讨论了某些以塞尔伯格积分为模型的超几何积分（包括 Felder & Silvotti 和 Dotsenko & Fateev 所描述的 BPZ 的二维 CFT 最小模型的 3 点和 4 点函数）（"库仑气体形式主义"）的分形延续。这是通过对积分的奇异性进行几何分析实现的。在积分是对称的（如塞尔伯格积分本身），或者更一般地说，我们称之为 "DF-对称 "的情况下，我们证明了一些表面奇点是可以消除的，这正是通过这些方法构建最小模型所需要的。

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

The Singularities of Selberg- and Dotsenko–Fateev-Like Integrals

We discuss the meromorphic continuation of certain hypergeometric integrals modeled on the Selberg integral, including the 3-point and 4-point functions of BPZ’s minimal models of 2D CFT as described by Felder & Silvotti and Dotsenko & Fateev (the “Coulomb gas formalism”). This is accomplished via a geometric analysis of the singularities of the integrands. In the case that the integrand is symmetric (as in the Selberg integral itself) or, more generally, what we call “DF-symmetric,” we show that a number of apparent singularities are removable, as required for the construction of the minimal models via these methods.

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

Annales Henri Poincaré 物理-物理：粒子与场物理

CiteScore

3.00

自引率

6.70%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society. The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.