On F-theory E₆ GUTs

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.