{"title":"3d ({\\mathcal {N}}=4\\ )理论的扭曲形式主义","authors":"Niklas Garner","doi":"10.1007/s11005-023-01758-9","DOIUrl":null,"url":null,"abstract":"<div><p>We describe the topological <i>A</i> and <i>B</i> twists of 3d <span>\\({\\mathcal {N}}=4\\)</span> theories of hypermultiplets gauged by <span>\\({\\mathcal {N}}=4\\)</span> vector multiplets as certain deformations of the holomorphic–topological (<i>HT</i>) twist of those theories, utilizing the twisted superfields of Aganagic–Costello–Vafa–McNamara describing <i>HT</i>-twisted 3d <span>\\({\\mathcal {N}}=2\\)</span> theories. We rederive many known results from this perspective, including state spaces on Riemann surfaces, deformations induced by flavor symmetries, the boundary VOAs of Costello–Gaiotto, and the category of line operators as proposed by Costello–Dimofte–Gaiotto–Hilburn–Yoo. Along the way, we show how the secondary product of local operators in the holomorphic–topological twist is related to the secondary product in the fully topological twist.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Twisted formalism for 3d \\\\({\\\\mathcal {N}}=4\\\\) theories\",\"authors\":\"Niklas Garner\",\"doi\":\"10.1007/s11005-023-01758-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We describe the topological <i>A</i> and <i>B</i> twists of 3d <span>\\\\({\\\\mathcal {N}}=4\\\\)</span> theories of hypermultiplets gauged by <span>\\\\({\\\\mathcal {N}}=4\\\\)</span> vector multiplets as certain deformations of the holomorphic–topological (<i>HT</i>) twist of those theories, utilizing the twisted superfields of Aganagic–Costello–Vafa–McNamara describing <i>HT</i>-twisted 3d <span>\\\\({\\\\mathcal {N}}=2\\\\)</span> theories. We rederive many known results from this perspective, including state spaces on Riemann surfaces, deformations induced by flavor symmetries, the boundary VOAs of Costello–Gaiotto, and the category of line operators as proposed by Costello–Dimofte–Gaiotto–Hilburn–Yoo. Along the way, we show how the secondary product of local operators in the holomorphic–topological twist is related to the secondary product in the fully topological twist.</p></div>\",\"PeriodicalId\":685,\"journal\":{\"name\":\"Letters in Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-01-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Letters in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11005-023-01758-9\",\"RegionNum\":3,\"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":"Letters in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11005-023-01758-9","RegionNum":3,"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}
Twisted formalism for 3d \({\mathcal {N}}=4\) theories
We describe the topological A and B twists of 3d \({\mathcal {N}}=4\) theories of hypermultiplets gauged by \({\mathcal {N}}=4\) vector multiplets as certain deformations of the holomorphic–topological (HT) twist of those theories, utilizing the twisted superfields of Aganagic–Costello–Vafa–McNamara describing HT-twisted 3d \({\mathcal {N}}=2\) theories. We rederive many known results from this perspective, including state spaces on Riemann surfaces, deformations induced by flavor symmetries, the boundary VOAs of Costello–Gaiotto, and the category of line operators as proposed by Costello–Dimofte–Gaiotto–Hilburn–Yoo. Along the way, we show how the secondary product of local operators in the holomorphic–topological twist is related to the secondary product in the fully topological twist.
期刊介绍:
The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.