Froggatt-Nielsen models from E8 in F-theory GUTs

TL;DR

This work investigates F-theory SU(5) GUTs where each SM generation originates from a distinct matter curve, all intersecting at an E8 point to leverage Froggatt-Nielsen flavours via singlet-vev induced hierarchies. A detailed scan under monodromy, Yukawa-rank, and proton-decay constraints yields a unique viable model only after imposing R-parity; the model provides a realistic pattern of quark masses and CKM-like mixing, and a Dirac/Seesaw-like neutrino sector with sizeable mixing. However, the approach encounters a no-go for hypercharge-based doublet-triplet splitting in 3-curve setups, implying that resolving the Higgs splitting problem requires either different local geometry or global completion. Overall, the paper demonstrates the potential and limitations of FN mechanics at an E8 point for realistic flavour in local F-theory GUTs, highlighting the need for global model considerations to address remaining phenomenological challenges.

Abstract

This paper studies F-theory SU(5) GUT models where the three generations of the standard model come from three different curves. All the matter is taken to come from curves intersecting at a point of enhanced E8 gauge symmetry. Giving a vev to some of the GUT singlets naturally implements a Froggatt-Nielsen approach to flavour structure. A scan is performed over all possible models and the results are filtered using phenomenological constraints. We find a unique model that fits observations of quark and lepton masses and mixing well. This model suffers from two drawbacks: R-parity must be imposed by hand and there is a doublet-triplet splitting problem.