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

TL;DR

This paper constructs SU(5) and SO(10) models from F-theory, demonstrating natural Yukawa couplings, gauge symmetry breaking, and solutions to the doublet-triplet splitting problem, with implications for fermion masses and unification.

Contribution

It presents novel F-theory models with natural Yukawa couplings, gauge symmetry breaking, and unification features, addressing longstanding issues like doublet-triplet splitting.

Findings

Yukawa couplings preserve U(1) symmetries at intersections

F-theory models achieve natural fermion mass generation

Yukawa unification occurs for specific fermion pairs

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.