Revision 2

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Title · changed: Revision 1: Which conformal field theories have a semiclassical gravity dual; Revision 2: Which conformal field theories have a semiclassical gravity dual?
Plain: Only special quantum theories behave as if they described a smooth curved space with ordinary gravity. The exact conditions that single them out are unknown.
Precise: Heemskerk, Penedones, Polchinski and Sully (2009) conjectured that a CFT with large central charge $c$ and a large gap $\Delta_{\mathrm{gap}}$ to single-trace operators of spin greater than 2 has a local Einstein-gravity dual. Determine necessary and sufficient conditions on CFT data for a semiclassical local bulk, and prove or refute the conjecture.
Settled by: A derivation from CFT axioms showing that large c and a large gap imply bulk locality and Einstein gravity at low energy, or a counterexample.
Kind: well-posed
Answer type: classification
References: (empty)
Literature status: partially-resolved
Status note: Causality and bootstrap bounds (2016-2023) derived suppression of higher-derivative couplings by $\Delta_{\mathrm{gap}}$; a full proof is missing.
Posed since: 2009

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