On hypercharge flux and exotics in F-theory GUTs

TL;DR

The paper investigates SU(5) GUTs in semi-local F-theory with multiple residual U(1) symmetries arising from small monodromies, examining how hypercharge flux drives doublet–triplet splitting and induces exotics. It shows that lifting exotics via singlet vevs generally breaks all U(1)s and can trigger proton-decay operators, motivating the imposition of an R-parity to suppress dangerous interactions while preserving MSSM-like gauge coupling unification at 1-loop. The work classifies matter curves under three monodromy factorisations (2+2+1, 3+1+1, 2+1+1+1) and analyzes single- and multi-curve generation scenarios, including Froggatt–Nielsen-based flavor textures. It also discusses Dirac and Majorana neutrino realizations and assesses the necessity of global completion to fix flux restrictions and potential discrete symmetries. The results indicate that, although advantageous, multiple U(1)s alone cannot fully forbid proton decay in lifted-exotics scenarios, and a robust discrete symmetry or alternative selection rules are required, with gauge coupling unification remaining viable under the proposed frameworks.

Abstract

We study SU(5) Grand Unified Theories within a local framework in F-theory with multiple extra U(1) symmetries arising from a small monodromy group. The use of hypercharge flux for doublet-triplet splitting implies massless exotics in the spectrum that are protected from obtaining a mass by the U(1) symmetries. We find that lifting the exotics by giving vacuum expectation values to some GUT singlets spontaneously breaks all the U(1) symmetries which implies that proton decay operators are induced. If we impose an additional R-parity symmetry by hand we find all the exotics can be lifted while proton decay operators are still forbidden. These models can retain the gauge coupling unification accuracy of the MSSM at 1-loop. For models where the generations are distributed across multiple curves we also present a motivation for the quark-lepton mass splittings at the GUT scale based on a Froggatt-Nielsen approach to flavour.