Extremal $1/2$ Calabi–Yau $3$-folds and six-dimensional F-theory applications

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Theoretical and Mathematical Physics Pub Date : 2020-03-04 DOI:10.4310/ATMP.2022.v26.n5.a6
Y. Kimura
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引用次数: 2

Abstract

We discuss a method for classifying the singularity types of 1/2 Calabi-Yau 3-folds, a family of rational elliptic 3-folds introduced in a previous study in relation to various U(1) factors in 6D F-theory models. A projective dual pair of del Pezzo manifolds recently studied by Mukai is used to analyze the singularity types. In particular, we studied the maximal rank seven singularity types of 1/2 Calabi-Yau 3-folds. The structures of the singular fibers are analyzed using blow-ups. Double covers of the 1/2 Calabi-Yau 3-folds yield elliptic Calabi-Yau 3-folds and applications to six-dimensional $N = 1$ F-theory on the Calabi-Yau 3-folds are also discussed. The deduced singular fibers have applications in studying the gauge groups formed in 6D F-theory compactifications. The blow-up methods used to analyze the singular fibers and sections utilized in this research might have applications in studying the U(1) factors and hypermultiplets charged under U(1) in 6D F-theory.
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极值$1/2$ Calabi-Yau $3$折叠和六维f理论的应用
本文讨论了一种划分1/2 Calabi-Yau 3-fold奇点类型的方法。1/2 Calabi-Yau 3-fold是在前人的研究中引入的与6D f理论模型中各种U(1)因子相关的有理椭圆型3-fold族。利用Mukai最近研究的del Pezzo流形的射影对偶对来分析奇异型。特别地,我们研究了1/2 Calabi-Yau 3-fold的极大秩7奇点类型。用放大法分析了奇异纤维的结构。讨论了1/2 Calabi-Yau 3-fold的双盖生成椭圆型Calabi-Yau 3-fold及其在六维$N = 1$ f理论中的应用。推导出的奇异纤维可用于研究六维f理论紧化中形成的规范群。本研究中用于分析奇异纤维和截面的爆破方法可能在研究6D f理论中U(1)因子和U(1)下带电的超重态方面具有应用价值。
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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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