# Compact F-theory GUTs with U(1)_{PQ}

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## 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 *μ* 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 [1], 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 [2] 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, though this analysis does not incorporate contributions from additional fluxes that will ultimately be needed for moduli stabilization. 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.

## Keywords

Strings and branes phenomenology## References

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