On hypercharge flux and exotics in F-theory GUTs

TL;DR

This paper investigates SU(5) GUTs in F-theory with multiple U(1) symmetries, focusing on hypercharge flux, exotics, and proton decay, proposing mechanisms to lift exotics while maintaining unification.

Contribution

It analyzes the impact of hypercharge flux and U(1) symmetries on exotics and proton decay, proposing solutions to lift exotics without breaking unification.

Findings

Exotics are protected by U(1) symmetries when using hypercharge flux.

Lifting exotics by VEVs breaks U(1)s and induces proton decay.

Imposing R-parity can lift exotics while forbidding proton decay operators.

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.