On Global Flipped SU(5) GUTs in F-theory

TL;DR

This work tackles the problem of realizing global flipped $SU(5)$ GUTs in F-theory by constructing an $SU(4)$ spectral divisor and analyzing its $(3,1)$ and $(2,2)$ factorizations to compute the chiral spectrum. The authors use a spectral-divisor framework motivated by heterotic/F-theory duality to obtain intrinsic net-chirality formulas, and they demonstrate that global divisor computations agree with semi-local spectral-cover results, even in vacua without heterotic duals. The key contributions include explicit global constructions of $SU(4)$ spectral divisors, matching chirality predictions $N_{f 16}=-(6c_1-t) ightharpoonup(2c_1-t)$ and $N_{f 10}=0$, and detailed factorization analyses for both $(3,1)$ and $(2,2)$ cases. This work strengthens the spectral-divisor program as a robust global tool for F-theory GUT model building and motivates further exploration of a CY4 index interpretation of chirality within this framework.

Abstract

We construct an SU(4) spectral divisor and its factorization of types (3,1) and (2,2) based on the construction proposed in [1]. We calculate the chiral spectra of flipped SU(5) GUTs by using the spectral divisor construction. The results agree with those from the analysis of semi-local spectral covers. Our computations provide an example for the validity of the spectral divisor construction and suggest that the standard heterotic formulae are applicable to the case of F-theory on an elliptically fibered Calabi-Yau fourfold with no heterotic dual.

Figures (1)

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