Heterotic/$F$-theory duality and Narasimhan–Seshadri equivalence

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
H. Clemens, S. Raby
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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.
异质性/$F$-理论二象性与Narasimhan-Seshadri等价
寻找具有wilsonline对称破缺的异杂模型的$F$-理论对偶,提出了在$F$-理论模型上实现$\mathbb{Z}_{2}$-作用的挑战,使得$\mathbb{Z}_{2}$-商是Calabi-Yau,且在$SU\左(5\右)_{规}$对称是Enriques $\ mathm {GUT}$曲面上。我们利用具有Yang-Mills连接的实$E_{8}$-束与其伴生的复全纯$E_{8}^{\mathbb{C}}$-束之间的Narasimhan-Seshadri等价的应用中的一个不太引人注意的选择,即由$E_{8}^{\mathbb{C}}$的复共轭实外自同构给出的等价,提出了一种新的方法来解决这个问题。紧实形式$E_{8}$上限制的琐碎性允许我们将其引入$\mathbb{Z}_{2}$-动作中,从而恢复$E_{8}$-以及$SU\左(5\右)_{规范}$-对称性,在此对称性上可以包裹威尔逊线。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
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.
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