A Global SU(5) F-theory model with Wilson line breaking

TL;DR

<3-5 sentence high-level summary> The paper develops a complete local-to-global construction of SU(5) GUTs in F-theory where GUT breaking is achieved by a discrete Wilson line on an Enriques surface, avoiding hypercharge flux corrections. It deploys the Tate divisor formalism to extend local Higgs-bundle data and G-fluxes, producing globally consistent models with U(1) symmetries and three chiral generations. The global completions reveal a spectrum with vector-like Higgs exotics and SU(5) adjoint exotics and analyze D3-brane tadpoles, identifying a minimal flux choice that cancels tadpoles with few anti-D3-branes. The study highlights challenges in attaining a fully realistic Higgs sector and proton stability within Wilson-line breaking and suggests future directions, including alternative base geometries and discrete symmetries to address mu-problem and proton decay. All mathematical notation is presented with delimiters as required.

Abstract

We engineer compact SU(5) Grand Unified Theories in F-theory in which GUT-breaking is achieved by a discrete Wilson line. Because the internal gauge field is flat, these models avoid the high scale threshold corrections associated with hypercharge flux. Along the way, we exemplify the `local-to-global' approach in F-theory model building and demonstrate how the Tate divisor formalism can be used to address several challenges of extending local models to global ones. These include in particular the construction of G-fluxes that extend non-inherited bundles and the engineering of U(1) symmetries. We go beyond chirality computations and determine the precise (charged) massless spectrum, finding exactly three families of quarks and leptons but excessive doublet and/or triplet pairs in the Higgs sector (depending on the example) and vector-like exotics descending from the adjoint of SU(5)_{GUT}. Understanding why vector-like pairs persist in the Higgs sector without an obvious symmetry to protect them may shed light on new solutions to the mu problem in F-theory GUTs.