Generalized Symmetries, Gravity, and the Swampland

TL;DR

This paper explores how generalized global symmetries in quantum field theories are broken or gauged in quantum gravity contexts, especially within M-theory compactifications, revealing constraints on gauge group structures and higher symmetries.

Contribution

It explicitly demonstrates the breaking of higher symmetries in 7D and 5D M-theory vacua and derives conditions for gauging and global structures of gauge groups from gravitational backgrounds.

Findings

Higher symmetries are trivialized by gravitational degrees of freedom.

Gluing conditions determine the global structure of gauge groups.

Constraints on gauge group forms in F-theory models derived from Calabi-Yau compactifications.

Abstract

Generalized global symmetries are a common feature of many quantum field theories decoupled from gravity. By contrast, in quantum gravity / the Swampland program, it is widely expected that all global symmetries are either gauged or broken, and this breaking is in turn related to the expected completeness of the spectrum of charged states in quantum gravity. We investigate the fate of such symmetries in the context of 7D and 5D vacua realized by compact Calabi-Yau spaces with localized singularities in M-theory. We explicitly show how gravitational backgrounds support additional dynamical degrees of freedom which trivialize (i.e.,"break") the higher symmetries of the local geometric models. Local compatability conditions across these different sectors lead to gluing conditions for gauging higher-form and (in the 5D case) higher-group symmetries. This also leads to a preferred global structure of the gauge group and higher-form gauge symmetries. In cases based on a genus-one fibered Calabi-Yau space, we also get an F-theory model in one higher dimension with corresponding constraints on the global form of the gauge group.