U(1) symmetries in F-theory GUTs with multiple sections

TL;DR

This work develops a systematic global construction of F-theory GUTs with Abelian $U(1)$ symmetries by employing factorised Tate models that yield extra global sections. It presents explicit realizations for $SU(5)\times U(1)_X$ and $SU(5)\times U(1)_{PQ}$, resolves the associated singularities, and derives matter charges and $G_4$-fluxes directly from geometry. A key finding is the appearance of charged singlets in the $U(1)_{PQ}$ model that do not fit into a single $E_8$ decomposition, highlighting global effects beyond local model intuition. The paper also recasts these constructions in a $P[1,1,2]$-fibration framework, connecting to Morrison–Taylor two-section formalisms and split spectral cover limits, and sets the stage for extending to multiple $U(1)$ factors. Overall, the results enable global realizations of local F-theory phenomenology, including richer Yukawa structures and novel singlet sectors, with potential implications for proton decay control and flavor physics.

Abstract

We present a systematic construction of F-theory compactifications with Abelian gauge symmetries in addition to a non-Abelian gauge group G. The formalism is generally applicable to models in global Tate form but we focus on the phenomenologically interesting case of G=SU(5). The Abelian gauge factors arise due to extra global sections resulting from a specific factorisation of the Tate polynomial which describes the elliptic fibration. These constructions, which accommodate up to four different U(1) factors, are worked out in detail for the two possible embeddings of a single U(1) factor into E8, usually denoted SU(5) x U(1)_X and SU(5) x U(1)_PQ. The resolved models can be understood either patchwise via a small resolution or in terms of a P_{1,1,2}[4] description of the elliptic fibration. We derive the U(1) charges of the fields from the geometry, construct the U(1) gauge fluxes and exemplify the structure of the Yukawa interaction points. A particularly interesting result is that the global SU(5) x U(1)_PQ model exhibits extra SU(5)-singlet states which are incompatible with a single global decomposition of the 248 of E8. The states in turn lead to new Yukawa type couplings which have not been considered in local model building.

Figures (3)

• Figure 1: Schematic drawing of the ${\bf 10}^{(1)} \, {\bf \overline{10}}^{(2)}{\bf 1}$ Yukawa coupling in the case of the 4-1 split.
• Figure 2: Schematic drawing of the $\mathbf{10}^{(1)}$$\mathbf{\overline{10}}^{(2)}$$\mathbf{1}$ Yukawa coupling in the case of the 3-2 split.
• Figure 3: Schematic drawing of the fibre over the charge 10 and 5 singlet curves. The green and blue crosses indicate the intersections with $Z$ and $S$, respectively. In the case of the charge $10$ singlet, $S$ becomes one of the $\mathbb{P}^1_{\,}$'s, which we indicate by the blue ball.