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

TL;DR

This work tackles the Yukawa hierarchy problem in local F-theory GUTs by enabling a minimal flux mechanism: a $U(1)$ flux through two matter curves of the same GUT representation cancels on average, distributing fermions between the curves to permit hierarchical Yukawas without requiring self-intersecting curves. It provides explicit local $SO(10)$ and $SU(5)$ constructions on del Pezzo surfaces in which three generations emerge, exotics are controlled, and Yukawa textures yield suppressed third-generation quark mixing alongside potentially large lepton mixing, all while preserving gauge coupling unification. The approach offers a concrete geometric route to realistic fermion masses and mixings, motivating quantitative fits and global embeddings in F-theory compactifications. Key result: average flux cancellation on matter-curves can realize viable Yukawa structures in F-theory GUTs with MSSM-like spectra.

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.

Figures (3)

• Figure 1: Triple intersection of two curves $\Sigma_1$ and $\Sigma_2$, with two and one generations of $SO(10)$ without fluxes going through them. Dashed lines represent fermions linked by a Yukawa coupling. Most Yukawa couplings are forbidden.
• Figure 2: Sketch of the structure of the $B-L$ fluxed $SO(10)$ model. Dashed lines represent fermions linked by a Yukawa coupling. Yukawa couplings for all fermions are allowed.
• Figure 3: Sketch of the structure of the hypercharge fluxed $SU(5)$ model.