{"title":"作为塞伯格对偶性的福氏 ODEs","authors":"Sergio Cecotti","doi":"10.4310/atmp.2023.v27.n8.a4","DOIUrl":null,"url":null,"abstract":"The classical theory of Fuchsian differential equations is largely equivalent to the theory of Seiberg dualities for quiver SUSY gauge theories. In particular: <i>all</i> known integral representations of solutions, and their connection formulae, are immediate consequences of (analytically continued) Seiberg duality in view of the dictionary between linear ODEs and gauge theories with $4$ supersymmetries. The purpose of this divertissement is to explain “physically” this remarkable relation in the spirit of Physical Mathematics. The connection goes through a “mirror-theoretic” identification of irreducible logarithmic connections on $\\mathbb{P}^1$ with would-be BPS dyons of 4d $\\mathcal{N} = 2 \\: SU(2)$ SYM coupled to a certain Argyres–Douglas “matter”. When the underlying bundle is trivial, i.e. the log‑connection is a Fuchs system, the world-line theory of the dyon simplifies and the action of Seiberg duality on the Fuchsian ODEs becomes quite explicit. The duality action is best described in terms of Representation Theory of Kac–Moody Lie algebras (and their affinizations).","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fuchsian ODEs as Seiberg dualities\",\"authors\":\"Sergio Cecotti\",\"doi\":\"10.4310/atmp.2023.v27.n8.a4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The classical theory of Fuchsian differential equations is largely equivalent to the theory of Seiberg dualities for quiver SUSY gauge theories. In particular: <i>all</i> known integral representations of solutions, and their connection formulae, are immediate consequences of (analytically continued) Seiberg duality in view of the dictionary between linear ODEs and gauge theories with $4$ supersymmetries. The purpose of this divertissement is to explain “physically” this remarkable relation in the spirit of Physical Mathematics. The connection goes through a “mirror-theoretic” identification of irreducible logarithmic connections on $\\\\mathbb{P}^1$ with would-be BPS dyons of 4d $\\\\mathcal{N} = 2 \\\\: SU(2)$ SYM coupled to a certain Argyres–Douglas “matter”. When the underlying bundle is trivial, i.e. the log‑connection is a Fuchs system, the world-line theory of the dyon simplifies and the action of Seiberg duality on the Fuchsian ODEs becomes quite explicit. The duality action is best described in terms of Representation Theory of Kac–Moody Lie algebras (and their affinizations).\",\"PeriodicalId\":50848,\"journal\":{\"name\":\"Advances in Theoretical and Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-08-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Theoretical and Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.4310/atmp.2023.v27.n8.a4\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.4310/atmp.2023.v27.n8.a4","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
The classical theory of Fuchsian differential equations is largely equivalent to the theory of Seiberg dualities for quiver SUSY gauge theories. In particular: all known integral representations of solutions, and their connection formulae, are immediate consequences of (analytically continued) Seiberg duality in view of the dictionary between linear ODEs and gauge theories with $4$ supersymmetries. The purpose of this divertissement is to explain “physically” this remarkable relation in the spirit of Physical Mathematics. The connection goes through a “mirror-theoretic” identification of irreducible logarithmic connections on $\mathbb{P}^1$ with would-be BPS dyons of 4d $\mathcal{N} = 2 \: SU(2)$ SYM coupled to a certain Argyres–Douglas “matter”. When the underlying bundle is trivial, i.e. the log‑connection is a Fuchs system, the world-line theory of the dyon simplifies and the action of Seiberg duality on the Fuchsian ODEs becomes quite explicit. The duality action is best described in terms of Representation Theory of Kac–Moody Lie algebras (and their affinizations).
期刊介绍:
Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.