Yukawa Structure from U(1) Fluxes in F-theory Grand Unification

TL;DR

This paper explores how U(1) fluxes in F-theory GUTs can naturally produce hierarchical Yukawa couplings by redistributing fermion content, offering a promising path toward realistic grand unified models with observed fermion hierarchies.

Contribution

It introduces a novel mechanism involving U(1) fluxes passing through matter curve pairs to generate fermion hierarchies in F-theory GUTs, especially for SO(10) models.

Findings

Hierarchical Yukawas achieved through flux-induced fermion reshuffling.

Specific local F-theory models with MSSM content on del Pezzo surfaces.

Predicted small third-generation quark mixing as a potential signature.

Abstract

In F-theory GUT constructions Yukawa couplings necessarily take place at the intersection of three matter curves. For generic geometric configurations this gives rise to problematic Yukawa couplings unable to reproduce the observed hierarchies. We point out that if the U(1)_{B-L}/U(1)_Y flux breaking the SO(10)/SU(5) GUT symmetry is allowed to go through pairs of matter curves with the same GUT representation, the quark/lepton content is redistributed in such a way that all quark and leptons are allowed to have hierarchical Yukawas. This reshuffling of fermions is quite unique and is particularly elegant for the case of three generations and SO(10). Specific local F-theory models with SO(10) or SU(5) living on a del Pezzo surface with appropriate bundles and just the massless content of the MSSM are described. We point out that the smallness of the 3rd generation quark mixing predicted by this scheme (together with gauge coupling unification) could constitute a first hint of an underlying F-theory grand unification.