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

We construct six-dimensional (6D) F-theory models in which discrete ℤ5, ℤ4, ℤ3, and ℤ2 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 ℤ5 gauge group. We construct 6D F-theory models with a discrete ℤ5 gauge group over the del Pezzo surfaces, as well as over ℙ1 × ℙ1 and ℙ2. We also discuss some applications to four-dimensional F-theory models with discrete gauge symmetries.