Non-perturbative effects and Yukawa hierarchies in F-theory SU(5) Unification

TL;DR

This paper investigates how non-perturbative instanton effects in F-theory SU(5) models can generate hierarchical Yukawa couplings for lighter quark and lepton generations, aligning theoretical predictions with observed mass patterns.

Contribution

It reveals previously overlooked instanton contributions that induce non-perturbative Yukawa corrections, explaining fermion mass hierarchies in F-theory GUTs.

Findings

Non-perturbative effects induce hierarchical Yukawa couplings.

Hypercharge flux modifies wavefunction profiles without affecting holomorphic Yukawas.

Combined effects explain second and third generation fermion masses.

Abstract

Local SU(5) F-theory models lead naturally to Yukawa couplings for the third generation of quarks and leptons, but inducing Yukawas for the lighter generations has proven elusive. Corrections coming from gauge fluxes fail to generate the required couplings, and naively the same applies to instanton effects. We nevertheless revisit the effect of instantons in F-theory GUT constructions and find that contributions previously ignored in the literature induce the leading non-perturbative corrections to the Yukawa couplings. We apply our results to the case of 10 x 5* x 5* couplings in local SU(5) F-theory GUTs, showing that non-perturbative effects naturally lead to hierarchical Yukawas. The hypercharge flux required to break SU(5) down to the SM does not affect the holomorphic Yukawas but does modify the profile of the wavefunctions, explaining the difference between the D-quark and lepton couplings at the unification scale. The combination of non-perturbative corrections and magnetic fluxes allows to describe the measured lepton and D-quark masses of second and third generations in the SM.