Compact F-theory GUTs with U(1)_PQ

TL;DR

This paper constructs F-theory SU(5) GUT models with a U(1)_PQ symmetry that prevents proton decay and addresses unification issues, providing detailed semi-local and global models with minimal exotics and viable neutrino candidates.

Contribution

It presents new semi-local and global F-theory GUT models incorporating U(1)_PQ symmetry, solving the unification problem and exploring exotic spectra and neutrino candidates.

Findings

Models with minimal non-GUT exotics satisfying D3-tadpole constraints.

Existence of models with U(1)_PQ symmetry that prevent proton decay.

Candidate right-handed neutrinos identified among SU(5) singlets.

Abstract

We construct semi-local and global realizations of SU(5) GUTs in F-theory that utilize a U(1)_PQ symmetry to protect against dimension four proton decay. Symmetries of this type, which assign charges to H_u and H_d that forbid a tree level \mu term, play an important role in scenarios for neutrino physics and gauge mediation that have been proposed in local F-theory model building. As demonstrated in arXiv:0906.4672, the presence of such a symmetry implies the existence of non-GUT exotics in the spectrum, when hypercharge flux is used to break the GUT group and to give rise to doublet-triplet splitting. These exotics are of precisely the right type to solve the unification problem in such F-theory models and might also comprise a non-standard messenger sector for gauge mediation. We present a detailed description of models with U(1)_PQ in the semi-local regime, which does not depend on details of any specific Calabi-Yau four-fold, and then specialize to the geometry of arXiv:0904.3932 to construct three-generation examples with the minimal allowed number of non-GUT exotics. Among these, we find a handful of models in which the D3-tadpole constraint can be satisfied without requiring the introduction of anti-D3-branes. Finally, because SU(5) singlets that carry U(1)_PQ charge may serve as candidate right-handed neutrinos or can be used to lift the exotics, we study their origin in compact models and motivate a conjecture for how to count their zero modes in a semi-local setting.