We consider realistic F-theory GUT models based on discrete family symmetries A 4 and S 3 , combined with SU(5) GUT, comparing our results to existing field theory models based on these groups. We provide an explicit calculation to support the emergence of the family symmetry from the discrete monodromies arising in F-theory. We work within the spectral cover picture where in the present context the discrete symmetries are associated to monodromies among the roots of a five degree polynomial and hence constitute a subgroup of the S 5 permutation symmetry. We focus on the cases of A 4 and S 3 subgroups, motivated by successful phenomenological models interpreting the fermion mass hierarchy and in particular the neutrino data. More precisely, we study the implications on the effective field theories by analysing the relevant discriminants and the topological properties of the polynomial coefficients, while we propose a discrete version of the doublet-triplet splitting mechanism.

Abstract:We discuss the origin of both non-Abelian discrete family symmetry and Abelian continuous family symmetry, as well as matter parity, from F-theory SUSY GUTs. We propose a minimal model based on the smallest GUT group SU(5), together with the non-Abelian family symmetry D 4 plus an Abelian family symmetry, where fluxes are responsible for doublet-triplet splitting, leading to a realistic low energy spectrum with phenomenologically acceptable quark and lepton masses and mixing. We show how a Z 2 matter parity emerging from F-theory can suppress proton decay while allowing neutronantineutron oscillations, providing a distinctive signature of the set-up.

We interpret the 750-760 GeV diphoton resonance as one or more of the spinless components of a singlet superfield arising from the three 27-dimensional representations of E 6 in F-theory, which also contain three copies of colour-triplet charge ∓1/3 vector-like fermions D i ,D i and inert Higgs doublets to which the singlets may couple. For definiteness we consider (without change) a model that was proposed some time ago which contains such states, as well as bulk exotics, leading to gauge coupling unification. The smoking gun prediction of the model is the existence of other similar spinless resonances, possibly close in mass to 750-760 GeV, decaying into diphotons, as well as the three families of vector-like fermions D i ,D i .

We discuss R-parity violation (RPV) in semi-local and local F-theory constructions. We first present a detailed analysis of all possible combinations of RPV operators arising from semi-local F-theory spectral cover constructions, assuming an SU(5) GUT. We provide a classification of all possible allowed combinations of RPV operators originating from operators of the form 10 ·5 ·5, including the effect of U(1) fluxes with global restrictions. We then relax the global constraints and perform explicit computations of the bottom/tau and RPV Yukawa couplings, at an SO(12) local point of enhancement in the presence of general fluxes subject only to local flux restrictions. We compare our results to the experimental limits on each allowed RPV operator, and show that operators such as LLe c , LQd c and u c d c d c may be present separately within current bounds, possibly on the edge of observability, suggesting lepton number violation or neutron-antineutron oscillations could constrain F-theory models.

We study low energy implications of F-theory GUT models based on SU(5) extended by a $$U(1)'$$ U ( 1 ) ′ symmetry which couples non-universally to the three families of quarks and leptons. This gauge group arises naturally from the maximal exceptional gauge symmetry of an elliptically fibred internal space, at a single point of enhancement, $$E_8\supset SU(5)\times SU(5)'\supset SU(5)\times U(1)^4.$$ E 8 ⊃ S U ( 5 ) × S U ( 5 ) ′ ⊃ S U ( 5 ) × U ( 1 ) 4 . Rank-one fermion mass textures and a tree-level top quark coupling are guaranteed by imposing a $$Z_2$$ Z 2 monodromy group which identifies two abelian factors of the above breaking sequence. The $$U(1)'$$ U ( 1 ) ′ factor of the gauge symmetry is an anomaly free linear combination of the three remaining abelian symmetries left over by $$Z_2$$ Z 2 . Several classes of models are obtained, distinguished with respect to the $$U(1)'$$ U ( 1 ) ′ charges of the representations, and possible extra zero modes coming in vector-like representations. The predictions of these models are investigated and are compared with the LHC results and other related experiments. Particular cases interpreting the B-meson anomalies observed in LHCb and BaBar experiments are also discussed.