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

TL;DR

This paper establishes a new consistency condition for 8d supergravity theories with non-trivial gauge group structures, linking anomaly considerations to geometric properties and constraining possible string theory realizations.

Contribution

It introduces an anomaly-based criterion involving the $Z$ 1-form symmetry that determines the consistency of 8d theories with non-simply-connected gauge groups, connecting field theory and geometry.

Findings

Most 8d theories with gauge group $G/Z$ are inconsistent when coupled to gravity.

The condition aligns with geometric properties of elliptic K3 surfaces in F-theory.

Constraints on gauge groups in 8d string models are identified.

Abstract

We present a consistency condition for 8d ${\cal N} = 1$ 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.