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

We construct six-dimensional (6D) F-theory models in which discrete Z(5), Z(4), Z(3), and 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 Z(5) gauge group. We construct 6D F-theory models with a discrete Z(5) gauge group over the del Pezzo surfaces, as well as over P-1 x P-1 and P-2. We also discuss some applications to four-dimensional F-theory models with discrete gauge symmetries.