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Title: Absence of global symmetries in quantum gravity outside anti-de Sitter
Plain: 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: 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.
Settled by: A proof using flat-space or de Sitter quantum gravity principles (S-matrix, black hole evaporation, or a dual description), or a counterexample.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: partially-resolved
Status note: Proven in AdS/CFT (Harlow, Ooguri 2018) and in perturbative string theory (Banks, Dixon 1988); open in flat and de Sitter space.
Posed since: 1988