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

TL;DR

This paper identifies discrete gauge symmetries in F-theory compactifications on genus-one fibered Calabi-Yau 4-folds without sections, introducing a general method to construct multisections and determine resulting symmetries.

Contribution

It presents a new method to obtain multisections in genus-one fibered Calabi-Yau manifolds, enabling the determination of discrete gauge symmetries in F-theory models.

Findings

Discrete $bZ_5$, $bZ_4$, $bZ_3$, $bZ_2$ symmetries identified

Constructed Calabi-Yau 4-folds using Fano manifolds and covers

Method for calculating multisection degrees established

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.