Flavor Hierarchy From F-theory

TL;DR

This work shows that flavor hierarchies in MSSM-like models can emerge naturally from the local geometry of F-theory GUTs with background flux. A leading rank-one Yukawa structure is enforced by a local $U(1)$ symmetry at brane intersections, while subleading distortions from fluxes generate hierarchical Yukawas controlled by $\varepsilon \sim \alpha_{GUT}^{1/2}$, producing CKM textures with powers of $\varepsilon$ and realistic fermion mass hierarchies. The analysis distinguishes derivative- and flux-driven perturbations, yielding two hierarchical patterns (DER and FLX) and a Froggatt–Nielsen-like CKM structure dominated by charges (3,2,0). The results align with observed quark and charged-lepton spectra after modest RG running, suggesting that the minimal geometric data of F-theory GUTs can account for the flavor puzzle while offering testable links between compactification geometry, flux, and low-energy flavor phenomenology.

Abstract

It has recently been shown that F-theory based constructions provide a potentially promising avenue for engineering GUT models which descend to the MSSM. In this note we show that in the presence of background fluxes, these models automatically achieve hierarchical Yukawa matrices in the quark and lepton sectors. At leading order, the existence of a U(1) symmetry which is related to phase rotations of the internal holomorphic coordinates at the brane intersection point leads to rank one Yukawa matrices. Subleading corrections to the internal wave functions from variations in the background fluxes generate small violations of this U(1), leading to hierarchical Yukawa structures reminiscent of the Froggatt-Nielsen mechanism. The expansion parameter for this perturbation is in terms of alpha_(GUT)^(1/2). Moreover, we naturally obtain a hierarchical CKM matrix with V_(12) ~ V_(21) ~ epsilon, V_(23) ~ V_(32) ~ epsilon^(2), V_(13) ~ V_(31) ~ epsilon^(3), where epsilon ~ alpha_(GUT)^(1/2), in excellent agreement with observation.