New Global F-theory GUTs with U(1) symmetries

TL;DR

This work constructs globally consistent F-theory GUTs with gauge group $SU(5)\times U(1)$ by specifying a fully resolved Calabi-Yau fourfold and a compatible $G_4$-flux. Unlike many local or $E_8$-based constructions, the model does not descend from a higgsed $E_8$ and lies outside the standard split-spectral-cover framework, enabling a wealth of abelian structure and avoiding recent no-go results for hypercharge flux. The authors show that a nontrivial Mordell-Weil group, including a rational $U(1)$ generator, yields a rich matter spectrum with Yukawa couplings allowed and proton-decay operators forbidden, while expressing the 4D chiral indices in terms of three-dimensional Chern-Simons terms derived from the vertical $G_4$-flux. This provides a concrete, computable global example of an F-theory GUT with abelian factors, offering a viable route around earlier phenomenological obstacles and a calculable link between geometry, fluxes, and 4D chirality.

Abstract

We construct global F-theory GUTs with SU(5) x U(1) gauge group defined by specifying a fully resolved Calabi-Yau fourfold and consistent four-form G-flux. Its specific U(1) charged matter spectrum allows the desired Yukawa couplings, but forbids dangerous proton decay operators. The model we find: (1) does not follow from an underlying higgsed E8 gauge group (2) leaves the class of theories that can be analyzed with current split-spectral cover techniques. This avoids recently proposed no-go theorems for models with hypercharge flux, as required to break the GUT group. The appearance of additional fields is related geometrically to considering a more general class of sections and 4-1 splits. We show explicitly that the four-dimensional chiral matter index can still be computed using three-dimensional one-loop Chern-Simons terms.

Figures (2)

• Figure 1: The three different relative orientations of the $I_5$ discriminant and two sections $\sigma_0$, $\sigma_1$. This notion matches the splitting of the spectral cover if and only if the spectral cover unbroken gauge group is the low-energy effective $SU(5)\times U(1)$.
• Figure 2: The toric ambient space fiber $C_0$, that is, one of the five irreducible components of $\pi^{-1}([h_0:h_1:0])$.