Discrete gauge groups in certain F-theory models in six dimensions

Abstract

We construct six-dimensional (6D) F-theory models in which discrete ${\mathbb{Z}}_5,{\mathbb{Z}}_4,{\mathbb{Z}}_3,$ and ${\mathbb{Z}}_2$ gauge symmetries arise. We demonstrate that a special family of "Fano 3-folds" is a useful tool for constructing the aforementioned models. The geometry of Fano 3-folds in the constructions of models can be useful for understanding discrete gauge symmetries in 6D F-theory compactifications. We argue that the constructions of the aforementioned models are applicable to Calabi-Yau genus-one fibrations over any base space, except models with a discrete ${\mathbb{Z}}_5$ gauge group. We construct 6D F-theory models with a discrete ${\mathbb{Z}}_5$ gauge group over the del Pezzo surfaces, as well as over ${\mathbb{P}}^1\times {\mathbb{P}}^1$ and ${\mathbb{P}}^2$. We also discuss some applications to four-dimensional F-theory models with discrete gauge symmetries.

arXiv comment19 pages, minor changes and minor typos corrected

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