{"title":"Heterotic/$F$-theory duality and Narasimhan–Seshadri equivalence","authors":"H. Clemens, S. Raby","doi":"10.4310/atmp.2021.v25.n5.a2","DOIUrl":null,"url":null,"abstract":"Finding the $F$-theory dual of a Heterotic model with Wilson-line symmetry breaking presents the challenge of achieving the dual $\\mathbb{Z}_{2}$-action on the $F$-theory model in such a way that the $\\mathbb{Z}_{2}$-quotient is Calabi-Yau with an Enriques $\\mathrm{GUT}$ surface over which $SU\\left(5\\right)_{gauge}$ symmetry is maintained. We propose a new way to approach this problem by taking advantage of a little-noticed choice in the application of Narasimhan-Seshadri equivalence between real $E_{8}$-bundles with Yang-Mills connection and their associated complex holomorphic $E_{8}^{\\mathbb{C}}$-bundles, namely the one given by the real outer automorphism of $E_{8}^{\\mathbb{C}}$ by complex conjugation. The triviality of the restriction on the compact real form $E_{8}$ allows one to introduce it into the $\\mathbb{Z}_{2}$-action, thereby restoring $E_{8}$- and hence $SU\\left(5\\right)_{gauge}$ -symmetry on which the Wilson line can be wrapped.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.4310/atmp.2021.v25.n5.a2","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}
引用次数: 6
Abstract
Finding the $F$-theory dual of a Heterotic model with Wilson-line symmetry breaking presents the challenge of achieving the dual $\mathbb{Z}_{2}$-action on the $F$-theory model in such a way that the $\mathbb{Z}_{2}$-quotient is Calabi-Yau with an Enriques $\mathrm{GUT}$ surface over which $SU\left(5\right)_{gauge}$ symmetry is maintained. We propose a new way to approach this problem by taking advantage of a little-noticed choice in the application of Narasimhan-Seshadri equivalence between real $E_{8}$-bundles with Yang-Mills connection and their associated complex holomorphic $E_{8}^{\mathbb{C}}$-bundles, namely the one given by the real outer automorphism of $E_{8}^{\mathbb{C}}$ by complex conjugation. The triviality of the restriction on the compact real form $E_{8}$ allows one to introduce it into the $\mathbb{Z}_{2}$-action, thereby restoring $E_{8}$- and hence $SU\left(5\right)_{gauge}$ -symmetry on which the Wilson line can be wrapped.
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.