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

TL;DR

This paper investigates how fluxes and instanton effects influence Yukawa couplings in local F-theory models, revealing mechanisms for fermion mass hierarchies and addressing the D-quark and Lepton mass differences.

Contribution

It demonstrates that non-perturbative effects induce Yukawa corrections without depending on magnetic fluxes, and proposes a wavefunction normalization approach to explain fermion mass differences.

Findings

Instanton effects induce Yukawa corrections.

Non-perturbative effects do not alter holomorphic Yukawas.

Hypercharge flux explains D-quark and Lepton mass differences.

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.