Flipped SU(5) GUTs from E_8 Singularities in F-theory

TL;DR

This work constructs supersymmetric flipped $SU(5)$ GUTs from $E_8$ singularities in F-theory by unfolding to an $SO(10)$ locus encoded in an $SU(4)$ spectral cover. To introduce adjustable chirality, the authors explore two factorizations of the cover, $(3,1)$ and $(2,2)$, and turn on a massless $U(1)_X$ flux to break $SO(10)$ to $SU(5)\times U(1)_X$, yielding a flipped $SU(5)$ framework. They develop the spectral-cover flux formalism for each factorization, compute the D3-tadpole contributions via the refined Euler characteristic $\chi(X_4)$ and $\Gamma^2$, and present explicit models on $dP_2$ and $dP_7$ Calabi–Yau backgrounds, achieving three- to four-generation examples with varying flux restrictions. The results demonstrate that the combination of cover factorization and $U(1)_X$ flux provides concrete, phenomenologically viable flipped $SU(5)$ spectra, though global issues such as the singlet Higgs realization and potential exotics remain as future challenges.

Abstract

In this paper we construct supersymmetric flipped SU(5) GUTs from E_8 singularities in F-theory. We start from an SO(10) singularity unfolded from an E_8 singularity by using an SU(4) spectral cover. To obtain realistic models, we consider (3,1) and (2,2) factorizations of the SU(4) cover. After turning on the massless U(1)_X gauge flux, we obtain the SU(5) X U(1)_X gauge group. Based on the well-studied geometric backgrounds in the literature, we demonstrate several models and discuss their phenomenology.

Figures (1)

• Figure 1: The extended $E_8$ Dynkin diagram and indices