Abelian Gauge Fluxes and Local Models in F-Theory

TL;DR

The paper addresses the challenge of realizing MSSM-like physics in local F-theory GUTs by constructing Abelian $U(1)^2$ gauge fluxes. It proves a no-go result for exotic-free fluxes in the $G_S=SO(10)$ case and provides explicit supersymmetric flux constructions for $G_S=SU(6)$ built from two fractional line bundles that satisfy Donaldson–Uhlenbeck–Yau (DUY) stability. These fluxes induce curve-level fluxes that break enhanced gauge groups to the Standard Model factors and enable Higgs localization on specific curves, achieving doublet–triplet splitting in some sectors, though the minimal MSSM spectrum is challenging to obtain; non-minimal MSSM spectra with exotics decoupled via couplings on extra curves are demonstrated. Overall, the work shows that local F-theory models with carefully chosen $U(1)^2$ fluxes provide a viable route to MSSM-like physics, guiding the embedding into global geometries and informing curve-based spectrum engineering.

Abstract

We analyze the Abelian gauge fluxes in local F-theory models with G_S=SU(6) and SO(10). For the case of G_S=SO(10), there is a no-go theorem which states that for an exotic-free spectrum, there are no solutions for U(1)^2 gauge fluxes. We explicitly construct the U(1)^2 gauge fluxes with an exotic-free bulk spectrum for the case of G_S=SU(6). We also analyze the conditions for the curves supporting the given field content and discuss non-minimal spectra of the MSSM with doublet-triplet splitting.