SU(5) and SO(10) Models from F-Theory with Natural Yukawa Couplings

TL;DR

The work constructs semi-realistic F-theory GUTs based on SU(5) and SO(10) that preserve selection rules from extra U(1) symmetries at Yukawa points and generate SM masses via background fluxes. By turning on hypercharge and B-L fluxes, the GUT groups are broken to subgroups while arranging matter curves to keep U(1)a U(1)b symmetry constraints, enabling all Yukawa couplings and rank-one textures to be lifted by H-fluxes. Vector-like states provide heavy threshold corrections to align gauge couplings at the string scale and naturally address doublet-triplet splitting. In the SU(5) model, bottom-tau Yukawa unification is achieved; in the SO(10) models, top-bottom and tau-nu_tau unifications arise, with neutrino masses accommodated via a double seesaw mechanism, yielding a consistent low-energy MSSM-like spectrum.

Abstract

We construct the SU(5) and SO(10) models from F-theory. Turning on the U(1) fluxes, we can break the SU(5) gauge symmetry down to the Standard Model (SM) gauge symmetry, and break the SO(10) gauge symmetry down to the SU(3)_C X SU(2)_L X SU(2)_R X U(1)_{B-L} gauge symmetry. In particular, all the SM fermion Yukawa couplings preserve the enhanced U(1)_a X U(1)_b gauge or global symmetries at the triple intersections of the SM fermion and Higgs curves. And the SM fermion masses and mixings can be generated in the presence of background fluxes. In our models, the doublet-triplet splitting problem can be solved naturally. The additional vector-like particles can obtain heavy masses via the instanton effects or Higgs mechanism and then decouple at the high scale. The SM gauge couplings at the string scale, which are splitted due to the U(1) flux effects, can be explained by considering heavy threshold corrections from the extra vector-like particles. Moreover, in the SU(5) model, we have the Yukawa coupling unification for the bottom quark and tau lepton. In the SO(10) models, we have the Yukawa coupling unification for the top and bottom quarks, and the Yukawa coupling unification for the tau lepton and tau neutrino.