Absence of global symmetries in quantum gravity outside anti-de Sitter
In plain words
It is believed that quantum gravity forbids exact global symmetries, symmetries not tied to a force. This is proven only for spaces with negative vacuum energy and in perturbative string theory.
Precise statement
Harlow and Ooguri (2018) proved in AdS/CFT that bulk quantum gravity has no global symmetries and that the gauge charge spectrum is complete. Determine whether the same holds in asymptotically flat and de Sitter quantum gravity, including higher-form and non-invertible global symmetries.
What would settle it
A proof using flat-space or de Sitter quantum gravity principles (S-matrix, black hole evaporation, or a dual description), or a counterexample.
Status in the literature
Proven in AdS/CFT (Harlow, Ooguri 2018) and in perturbative string theory (Banks, Dixon 1988); open in flat and de Sitter space.