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

Anamaría Font, Luis E. Ibáñez, Fernando Marchesano, Diego Regalado

TL;DR

This work tackles the puzzle of generating realistic Yukawa couplings for lighter fermions in local F-theory SU(5) GUTs by incorporating non-perturbative D3-instanton corrections through a holomorphic θ_n expansion, focusing on θ_0 and θ_2. By analyzing an SO(12) Yukawa point and solving corrected zero-mode equations, the authors derive a residue formula for holomorphic Yukawas and show that non-perturbative effects produce hierarchical patterns among the generations, while hypercharge flux differentiates D-quark and charged-lepton profiles. The study demonstrates that the combination of non-perturbative corrections and magnetic/hypercharge flux can reproduce observed second/third generation mass hierarchies and the b–τ splitting at the GUT scale, with Y_τ/Y_b ≈ 1.37 achievable for plausible flux ratios. These results provide a concrete mechanism to realize realistic fermion masses in a local F-theory GUT framework and suggest paths toward more complete global models and broader enhancement-point analyses.

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.

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

TL;DR

This work tackles the puzzle of generating realistic Yukawa couplings for lighter fermions in local F-theory SU(5) GUTs by incorporating non-perturbative D3-instanton corrections through a holomorphic θ_n expansion, focusing on θ_0 and θ_2. By analyzing an SO(12) Yukawa point and solving corrected zero-mode equations, the authors derive a residue formula for holomorphic Yukawas and show that non-perturbative effects produce hierarchical patterns among the generations, while hypercharge flux differentiates D-quark and charged-lepton profiles. The study demonstrates that the combination of non-perturbative corrections and magnetic/hypercharge flux can reproduce observed second/third generation mass hierarchies and the b–τ splitting at the GUT scale, with Y_τ/Y_b ≈ 1.37 achievable for plausible flux ratios. These results provide a concrete mechanism to realize realistic fermion masses in a local F-theory GUT framework and suggest paths toward more complete global models and broader enhancement-point analyses.

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.

Paper Structure

This paper contains 32 sections, 300 equations, 3 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Review of local F-theory models
  3. The SO(12) model
  4. Matter curves
  5. Worldvolume flux
  6. Perturbative zero modes
  7. Yukawa couplings
  8. Non-perturbative effects in local models
  9. The non-perturbative superpotential
  10. The corrected equations of motion
  11. Non-perturbative zero modes at the SO(12) point
  12. Zero modes for $n=0$
  13. Normalization and mixings of corrected zero modes
  14. Zero modes for $n=2$
  15. Yukawa couplings
  16. ...and 17 more sections

Figures (3)

  • Figure 1: Two possible scenarios for non-perturbative corrections to Yukawa couplings. In figure $i)$ the D3-brane instanton intersects a 7-brane that in turn intersects the 4-cycle $S_{GUT} = S_{MSSM}$. In figure $ii)$ the D3-instanton intersects only 7-brane divisors fully disconnected from $S_{GUT}$.
  • Figure 2: $\frac{m_\mu/m_\tau}{m_s/m_b}$ at the unification scale as a function of $\tilde{N}_Y/M$. The band shows the region consistent with the running of the low energy data up to the unification scale taken from ref.Ross:2007az. The dashed line is the Georgi-Jarlskog value GJ.
  • Figure 3: $Y_\tau/Y_b$ as a function of $M,N_Y$ for $N_a =-1(1)$ left(right). Flux choices are consistent with $\frac{m_\mu/m_\tau}{m_s/m_b}= 3(2.2)$ for upper(lower) plots.