AdS Bulk Locality from Sharp CFT Bounds

Understand

It is a long-standing conjecture that any CFT with a large central charge and a large gap $\Delta_{\text{gap}}$ in the spectrum of higher-spin single-trace operators must be dual to a local effective field theory in AdS.

• We prove a sharp form of this conjecture by deriving numerical bounds on bulk Wilson coefficients in terms of $\Delta_{\text{gap}}$ using the conformal bootstrap.
• Our bounds exhibit the scaling in $\Delta_{\text{gap}}$ expected from dimensional analysis in the bulk.
• Our main tools are dispersive sum rules that provide a dictionary between CFT dispersion relations and S-matrix dispersion relations in appropriate limits.