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arXiv · 1608.07219

Discrete Gauge Groups in F-theory Models on Genus-One Fibered Calabi-Yau 4-folds without Section

Yusuke Kimura
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Abstract

We determine the discrete gauge symmetries that arise in F-theory compactifications on examples of genus-one fibered Calabi-Yau 4-folds without a section. We construct genus-one fibered Calabi-Yau 4-folds using Fano manifolds, cyclic 3-fold covers of Fano 4-folds, and Segre embeddings of products of projective spaces. Discrete $\mathbb{Z}_5$, $\mathbb{Z}_4$, $\mathbb{Z}_3$ and $\mathbb{Z}_2$ symmetries arise in these constructions. We introduce a general method to obtain multisections for several constructions of genus-one fibered Calabi-Yau manifolds. The pullbacks of hyperplane classes under certain projections represent multisections to these genus-one fibrations. We determine the degrees of these multisections by computing the intersection numbers with fiber classes. As a result, we deduce the discrete gauge symmetries that arise in F-theory compactifications. This method applies to various Calabi-Yau genus-one fibrations.

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Yusuke Kimura. 2017-05-01. Discrete Gauge Groups in F-theory Models on Genus-One Fibered Calabi-Yau 4-folds without Section. https://doi.org/10.1007/jhep04(2017)168

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