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The exact conditions that single them out are unknown.","posed_since":"2009","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.","problem_ref":null,"references":"","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.","status_note":"Causality and bootstrap bounds (2016-2023) derived suppression of higher-derivative couplings by $\\Delta_{\\mathrm{gap}}$; a full proof is missing.","title":"Which conformal field theories have a semiclassical gravity 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