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

Understand

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.