A Note on Local GUT Models in F-Theory

TL;DR

This work extends local F-theory GUT constructions to non-minimal, higher-rank bulk gauge groups $G_S$ by placing seven-branes on a del Pezzo surface $S$ and turning on supersymmetric line bundles on $S$ and matter curves to break $G_S$ to GUT groups such as $SU(5)$ and $SO(10)$. Chiral spectra and Yukawa couplings are computed from bundle-valued cohomology and curve intersections, with Yukawas arising at codimension-three points of enhanced symmetry; GUT breaking to the MSSM is achieved via Abelian instantons. The authors provide explicit realizations: an $SU(5)$ GUT from $G_S=SU(6)$ and from $G_S=SO(10)$, a flipped $SU(5)$ attempt from $SU(6)$ (unsuccessful) and a successful one from $SO(10)$, and $SO(10)$ GUTs from $SO(12)$ and $E_6$, all with complete spectra and controlled exotics. These constructions demonstrate the viability of non-minimal local GUTs in F-theory and set the stage for global completions and phenomenological analysis, including exploring how instanton configurations break the bulk to MSSM and how Yukawa textures can be realized through curve intersections. \nKey techniques include using $dP_8$ surfaces, nontrivial line bundles on $S$ and curves, split bundles, and analysis of double-enhanced points to realize ${f 10}{f 10}{f 5}$ and related couplings.

Abstract

We construct non-minimal GUT local models in the F-theory configuration. The gauge group on the bulk G_S is one rank higher than the GUT gauge group. The line bundles on the curves are non-trivial to break G_S down to the GUT gauge groups. We demonstrate examples of SU(5) GUT from G_S=SU(6) and G_S=SO(10), the flipped SU(5) from G_S=SO(10), and the SO(10) GUT from G_S=SO(12) and G_S=E_6. We obtain complete GUT matter spectra and couplings, with minimum exotic matter contents. GUT gauge group breaking to MSSM is achievable by instanton configurations.