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

TL;DR

This paper constructs global SU(5) GUT models in F-theory using Wilson line breaking, avoiding certain threshold corrections, and explores the detailed spectrum and challenges of extending local models to global ones.

Contribution

It demonstrates a systematic approach to global F-theory GUT model building with Wilson line breaking and addresses technical challenges like G-flux extension and U(1) symmetry engineering.

Findings

Successfully constructed models with three families of quarks and leptons.

Identified issues with excess Higgs doublets/triplets and vector-like exotics.

Provided insights into the persistence of vector-like pairs and implications for the mu problem.

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.