{"title":"Examples of Deformed Spin(7)-Instantons/Donaldson–Thomas Connections","authors":"Udhav Fowdar","doi":"10.1007/s00220-024-05060-0","DOIUrl":null,"url":null,"abstract":"<div><p>We construct examples of deformed Hermitian Yang–Mills connections and deformed <span>\\(\\textrm{Spin}(7)\\)</span>-instantons (also called <span>\\(\\textrm{Spin}(7)\\)</span> deformed Donaldson–Thomas connections) on the cotangent bundle of <span>\\(\\mathbb {C}\\mathbb {P}^2\\)</span> endowed with the Calabi hyperKähler structure. Deformed <span>\\(\\textrm{Spin}(7)\\)</span>-instantons on cones over 3-Sasakian 7-manifolds are also constructed. We show that these can be used to distinguish between isometric structures and also between <span>\\(\\textrm{Sp}(2)\\)</span> and <span>\\(\\textrm{Spin}(7)\\)</span> holonomy cones. To the best of our knowledge, these are the first non-trivial examples of deformed <span>\\(\\textrm{Spin}(7)\\)</span>-instantons.\n</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 8","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05060-0.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s00220-024-05060-0","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We construct examples of deformed Hermitian Yang–Mills connections and deformed \(\textrm{Spin}(7)\)-instantons (also called \(\textrm{Spin}(7)\) deformed Donaldson–Thomas connections) on the cotangent bundle of \(\mathbb {C}\mathbb {P}^2\) endowed with the Calabi hyperKähler structure. Deformed \(\textrm{Spin}(7)\)-instantons on cones over 3-Sasakian 7-manifolds are also constructed. We show that these can be used to distinguish between isometric structures and also between \(\textrm{Sp}(2)\) and \(\textrm{Spin}(7)\) holonomy cones. To the best of our knowledge, these are the first non-trivial examples of deformed \(\textrm{Spin}(7)\)-instantons.
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The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.
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