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Flux and Instanton Effects in Local F-theory Models and Hierarchical Fermion Masses

Luis Aparicio, Anamaria Font, Luis E. Ibanez, Fernando Marchesano

TL;DR

This work analyzes how fluxes on 7-branes and non-perturbative effects deform Yukawa couplings in local F-theory models. It shows that holomorphic Yukawas are flux-independent at tree level, but non-perturbative effects from distant sectors or IASD fluxes can correct the Yukawas, potentially lifting their rank. The authors establish equivalences among 4d, 8d, and non-commutative descriptions (via a Seiberg-Witten map) and provide explicit computations in a $U(3)$ toy model to illustrate hierarchical structures. Crucially, wavefunction normalization and hypercharge flux reintroduce physically relevant differences between D-quark and lepton masses, offering a mechanism to reproduce observed fermion hierarchies within local F-theory GUTs. The results illuminate how non-perturbative physics and flux normalization jointly shape realistic flavor patterns in string-inspired models.

Abstract

We study the deformation induced by fluxes and instanton effects on Yukawa couplings involving 7-brane intersections in local F-theory constructions. In the absence of non-perturbative effects, holomorphic Yukawa couplings do not depend on open string fluxes. On the other hand instanton effects (or gaugino condensation on distant 7-branes) do induce corrections to the Yukawas. The leading order effect may also be captured by the presence of closed string (1,2) IASD fluxes, which give rise to a non-commutative structure. We check that even in the presence of these non-perturbative effects the holomorphic Yukawas remain independent of magnetic fluxes. Although fermion mass hierarchies may be obtained from these non-perturbative effects, they would give identical Yukawa couplings for D-quark and Lepton masses in SU(5) F-theory GUT's, in contradiction with experiment. We point out that this problem may be solved by appropriately normalizing the wavefunctions. We show in a simple toy model how the presence of hypercharge flux may then be responsible for the difference between D-quarks and Lepton masses in local SU(5) GUT's.

Flux and Instanton Effects in Local F-theory Models and Hierarchical Fermion Masses

TL;DR

This work analyzes how fluxes on 7-branes and non-perturbative effects deform Yukawa couplings in local F-theory models. It shows that holomorphic Yukawas are flux-independent at tree level, but non-perturbative effects from distant sectors or IASD fluxes can correct the Yukawas, potentially lifting their rank. The authors establish equivalences among 4d, 8d, and non-commutative descriptions (via a Seiberg-Witten map) and provide explicit computations in a toy model to illustrate hierarchical structures. Crucially, wavefunction normalization and hypercharge flux reintroduce physically relevant differences between D-quark and lepton masses, offering a mechanism to reproduce observed fermion hierarchies within local F-theory GUTs. The results illuminate how non-perturbative physics and flux normalization jointly shape realistic flavor patterns in string-inspired models.

Abstract

We study the deformation induced by fluxes and instanton effects on Yukawa couplings involving 7-brane intersections in local F-theory constructions. In the absence of non-perturbative effects, holomorphic Yukawa couplings do not depend on open string fluxes. On the other hand instanton effects (or gaugino condensation on distant 7-branes) do induce corrections to the Yukawas. The leading order effect may also be captured by the presence of closed string (1,2) IASD fluxes, which give rise to a non-commutative structure. We check that even in the presence of these non-perturbative effects the holomorphic Yukawas remain independent of magnetic fluxes. Although fermion mass hierarchies may be obtained from these non-perturbative effects, they would give identical Yukawa couplings for D-quark and Lepton masses in SU(5) F-theory GUT's, in contradiction with experiment. We point out that this problem may be solved by appropriately normalizing the wavefunctions. We show in a simple toy model how the presence of hypercharge flux may then be responsible for the difference between D-quarks and Lepton masses in local SU(5) GUT's.

Paper Structure

This paper contains 29 sections, 290 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Wavefunctions and Yukawa couplings in local F-theory models
  3. Local F-theory models from intersecting 7-branes
  4. Zero and massive modes at the intersection
  5. A $U(3)$ toy model
  6. Yukawa couplings
  7. Non-perturbative effects on intersecting 7-branes
  8. 4d approach
  9. 8d approach
  10. Non-commutative approach
  11. Corrected wavefunctions
  12. Wavefunctions and perturbation theory
  13. Relating commutative and non-commutative wavefunctions
  14. Wavefunctions and Yukawas in the non-commutative formalism
  15. Non-commutative zero modes in the $U(3)$ toy model
  16. ...and 14 more sections

Figures (1)

  • Figure 1: Sources of corrections to 7-brane Yukawas. Figure $a)$ represents the setup considered in mm09, where the Yukawas on a 7-brane stack wrapping the four-cycle $S_{GUT}$ are modified by the gaugino condensate on 7-branes on the distant four-cycle $S_{\rm np}$. Following km07, one may identify this setup with the one in figure $b)$, where the non-perturbative sector has been replaced by a $\beta$-deformation of the previous background. This new background contains IASD (1,2) background fluxes that induce a non-commutative deformation on $S_{GUT}$, in the sense of cchv09. This $\beta$-deformation is usually not-well defined around $S_{\rm np}$, and so typically the new three-fold $B_\beta$ can only be defined locally.