F-theory GUTs with U(1) Symmetries: Generalities and Survey

TL;DR

This paper analyzes SU(5) F-theory GUT models with additional U(1) symmetries, revealing constraints from anomaly cancellation and exploring spectral cover constructions to classify models with two U(1)s.

Contribution

It derives the Dudas-Palti relations within spectral cover models and provides a comprehensive survey of SU(5) GUT models with two U(1) symmetries in F-theory.

Findings

Identifies tension between unification and proton decay suppression with U(1) symmetries.

Derives DP relations explicitly in spectral cover models.

Classifies all spectral cover solutions with two U(1) symmetries.

Abstract

We study the structure of SU(5) F-theory GUT models that engineer additional U(1) symmetries. These are highly constrained by a set of relations observed by Dudas and Palti (DP) that originate from the physics of 4D anomaly cancellation. Using the DP relations, we find a general tension between unification and the suppression of dimension 5 proton decay when one or more U(1)'s are PQ symmetries and hypercharge flux is used to break the SU(5) GUT group. We then specialize to spectral cover models, whose global completions in F- theory we know how to construct. In that setting, we provide a technical derivation of the DP relations, construct spectral covers that yield all possible solutions to them, and provide a complete survey of spectral cover models for SU(5) GUTs that exhibit two U(1) symmetries.