# The Global Gauge Group Structure of F-theory Compactification with U(1)s

## TL;DR

This paper investigates the global gauge group structure in F-theory compactifications with U(1) factors, revealing geometric origins, charge constraints, and implications for Standard Model realizations and the F-theory swampland.

## Contribution

It uncovers the geometric origin of the global gauge group structure in F-theory with abelian factors and characterizes its impact on matter charges and gauge group realizations.

## Key findings

- F-theory models with the Standard Model algebra realize [SU(3)xSU(2)xU(1)]/Z6.
- The global gauge group structure constrains U(1) charges of matter.
- Charge constraints serve as criteria for the F-theory swampland.

## Abstract

We show that F-theory compactifications with abelian gauge factors generally exhibit a non-trivial global gauge group structure. The geometric origin of this structure lies with the Shioda map of the Mordell--Weil generators. This results in constraints on the U(1) charges of non-abelian matter consistent with observations made throughout the literature. In particular, we find that F-theory models featuring the Standard Model algebra actually realise the precise gauge group [SU(3)xSU(2)xU(1)]/Z6. Furthermore, we explore the relationship between the gauge group structure and geometric (un-)higgsing. In an explicit class of models, we show that, depending on the global group structure, an SU(2)xU(1) gauge theory can either unhiggs into an SU(2)xSU(2) or an SU(3)xSU(2) theory. We also study implications of the charge constraints as a criterion for the F-theory 'swampland'.