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.

19 pages, minor changes and minor typos corrected

References in corpus (16)

• Symmetries and Strings in Field Theory and Gravity
• GUTs and Exceptional Branes in F-theory - II: Experimental Predictions
• Stringy origin of non-Abelian discrete flavor symmetries
• F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds
• F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
• Non-Abelian Discrete Flavor Symmetries from Magnetized/Intersecting Brane Models
• Discrete Gauge Symmetries by Higgsing in four-dimensional F-Theory Compactifications
• Yukawas and discrete symmetries in F-theory compactifications without section
• A New Model for Elliptic Fibrations with a Rank One Mordell-Weil Group: I. Singular Fibers and Semi-Stable Degenerations
• Gauge Backgrounds and Zero-Mode Counting in F-Theory
• Tall sections from non-minimal transformations
• F-GUTs with Mordell-Weil U(1)'s
• Algebraic Cycles and Local Anomalies in F-Theory
• Generic matter representations in 6D supergravity theories
• Discrete Family Symmetry from F-Theory GUTs
• Mordell-Weil Torsion, Anomalies, and Phase Transitions

Cited by in corpus (2)

• The Geometry of SO(3), SO(5), and SO(6) models
• On genus one fibered Calabi-Yau threefolds with 5-sections