String Universality and Non-Simply-Connected Gauge Groups in 8d

Abstract

We present a consistency condition for 8d $\mathcal{N}=1$ supergravity theories with non-trivial global structure $G/Z$ for the non-Abelian gauge group, based on an anomaly involving the $Z$ 1-form center symmetry. The interplay with other Swampland criteria identifies the majority of 8d theories with gauge group $G/Z$, which have no string theory realization, as inconsistent quantum theories when coupled to gravity. While this condition is equivalent to geometric properties of elliptic K3 surfaces in F-theory compactifications, it constrains the unexplored landscape of gauge groups in other 8d string models.

7 pages, two-column style; v2: revised version with extended discussion on interplay between 1-form anomaly and worldsheet current algebra bounds, references added; v3: typos corrected