AdS bulk locality from sharp CFT bounds

It is a long-standing conjecture that any CFT with a large central charge and a large gap Delta(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(gap) using the conformal bootstrap. Our bounds exhibit the scaling in Delta(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. This dictionary allows us to apply recently-developed flat-space methods to construct positive CFT functionals. We show how AdS(4) naturally resolves the infrared divergences present in 4D flat-space bounds. Our results imply the validity of twice-subtracted dispersion relations for any S-matrix arising from the flat-space limit of AdS/CFT.

Automated summary

The paper proves a long-standing conjecture that any CFT with a large central charge and a large gap Delta(gap) in the spectrum of higher-spin single-trace operators must be dual to a local effective field theory in AdS. The authors derive numerical bounds on bulk Wilson coefficients in terms of Delta(gap) using the conformal bootstrap, and show how AdS(4) naturally resolves the infrared divergences present in 4D flat-space bounds. The results imply the validity of twice-subtracted dispersion relations for any S-matrix arising from the flat-space limit of AdS/CFT.