{"title":"计算环上可积分涡旋拓扑数的解析方法","authors":"Kaoru Miyamoto, Atsushi Nakamula","doi":"arxiv-2403.18264","DOIUrl":null,"url":null,"abstract":"An analytic method to calculate the vortex number on a torus is constructed,\nfocusing on analytic vortex solutions to the Chern-Simons-Higgs theory, whose\ngoverning equation is the so-called Jackiw-Pi equation. The equation is one of\nthe integrable vortex equations and is reduced to Liouville's equation. The\nrequirement of continuity of the Higgs field strongly restricts the\ncharacteristics and the fundamental domain of the vortices. Also considered are\nthe decompactification limits of the vortices on a torus, in which \"flux loss\"\nphenomena occasionally occur.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analytic Approach for Computation of Topological Number of Integrable Vortex on Torus\",\"authors\":\"Kaoru Miyamoto, Atsushi Nakamula\",\"doi\":\"arxiv-2403.18264\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An analytic method to calculate the vortex number on a torus is constructed,\\nfocusing on analytic vortex solutions to the Chern-Simons-Higgs theory, whose\\ngoverning equation is the so-called Jackiw-Pi equation. The equation is one of\\nthe integrable vortex equations and is reduced to Liouville's equation. The\\nrequirement of continuity of the Higgs field strongly restricts the\\ncharacteristics and the fundamental domain of the vortices. Also considered are\\nthe decompactification limits of the vortices on a torus, in which \\\"flux loss\\\"\\nphenomena occasionally occur.\",\"PeriodicalId\":501275,\"journal\":{\"name\":\"arXiv - PHYS - Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Mathematical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2403.18264\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2403.18264","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Analytic Approach for Computation of Topological Number of Integrable Vortex on Torus
An analytic method to calculate the vortex number on a torus is constructed,
focusing on analytic vortex solutions to the Chern-Simons-Higgs theory, whose
governing equation is the so-called Jackiw-Pi equation. The equation is one of
the integrable vortex equations and is reduced to Liouville's equation. The
requirement of continuity of the Higgs field strongly restricts the
characteristics and the fundamental domain of the vortices. Also considered are
the decompactification limits of the vortices on a torus, in which "flux loss"
phenomena occasionally occur.
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