Compact F-theory GUTs with U(1)PQ
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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 , 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  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.
KeywordsStrings and branes phenomenology