On F-theory E_6 GUTs

TL;DR

This paper develops semi-local to global F-theory constructions of $E_6$ GUTs that break to a rank-5 MSSM-like gauge group via a non-abelian flux $SU(2)\times U(1)^2$ on seven-branes. Using an $SU(3)$ spectral cover and its (2,1) and (1,1,1) factorizations, the authors compute matter localization, chirality, and flux-induced spectra on del Pezzo surfaces, while enforcing tadpole cancellation through the refined Euler characteristic $\chi(X_4)$ and the flux self-intersection $\Gamma^2$. They present explicit three-family models in $dP_2$ and $dP_7$, both with and without flux restrictions, highlighting the appearance of exotics and the need for additional symmetries to control them. The results demonstrate the viability and challenges of realizing MSSM-like physics from $E_6$ GUTs in F-theory, offering concrete geometric data and phenomenological pathways for further model building.

Abstract

We approach the Minimum Supersymmetric Standard Model (MSSM) from an E_6 GUT by using the spectral cover construction and non-abelian gauge fluxes in F-theory. We start with an E_6 singularity unfolded from an E_8 singularity and obtain E_6 GUTs by using an SU(3) spectral cover. By turning on SU(2) X U(1)^2 gauge fluxes, we obtain a rank 5 model with the gauge group SU(3) X SU(2) X U(1)^2. Based on the well-studied geometric backgrounds in the literature, we demonstrate several models and discuss their phenomenology.