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

TL;DR

This paper examines SU(5) F-theory GUTs with extra U(1) symmetries and derives the Dudas-Palti (DP) anomaly-based relations that constrain hypercharge flux distribution. It shows a fundamental tension between preserving gauge unification and suppressing dimension-5 proton decay when U(1)_{PQ} symmetries are present, and then specializes to spectral-cover constructions where DP relations can be derived and all DP-consistent solutions with up to two U(1)s are classified. A systematic survey identifies ten spectral-cover models with two U(1)s, characterized by a single parameter Δ=N-L that governs the exotic spectrum and the dimension-5 operators. The results indicate that, within the spectral-cover framework, only a subset of models can potentially reconcile unification with proton stability, highlighting the delicate balance between flux distribution, exotics, and singlet-induced mass terms. The work also provides extensive appendices with explicit model data and construction techniques that can guide global F-theory realizations.

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.