Towards a Realistic F-theory GUT

Abstract

We consider semi-local F-theory GUTs arising from a single E_8 point of local enhancement, leading to simple GUT groups based on E_6, SO(10) and SU(5) with SU(3), SU(4) and SU(5) spectral covers, respectively. Assuming the minimal Z_2 monodromy, we determine the homology classes and the associated spectra after flux breaking for each case. Our analysis includes the GUT singlets which have hitherto been ignored but which play a crucial role in phenomenology. Using these results we construct an E_6 based model that demonstrates, for the first time, that it is possible to construct a phenomenologically viable model which leads to the MSSM at low energies. The exotics that result from flux breaking all get a large mass when singlet fields acquire vacuum expectation values driven by D- and F-flatness. Due to the underlying GUT symmetry and the U(1)s descending from E_8, bare baryon- and lepton-number violating terms are forbidden up to and including dimension 5. As a result nucleon decay is naturally suppressed below present bounds. The mu-term is forbidden by the U(1) but is generated at the SUSY breaking scale when a further singlet field acquires a TeV scale vacuum expectation value, driven by the spontaneous breaking of the electroweak symmetry. After including the effect of flux and instanton corrections acceptable quark and charged lepton masses and mixing angles can be obtained. Neutrinos get a mass from the see-saw mechanism through their coupling to singlet neutrinos that acquire large Majorana mass as a result of the monodromy.