AdS bulk locality from sharp CFT bounds. (English) Zbl 1521.81292
Summary: It is a long-standing conjecture that any CFT with a large central charge and a large gap \(\Delta_{\mathrm{gap}}\) 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 \(\Delta_{\mathrm{gap}}\) using the conformal bootstrap. Our bounds exhibit the scaling in \(\Delta_{\mathrm{gap}}\) 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 \(\mathrm{AdS}_4\) 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.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81T35 | Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.) |
| 81T12 | Effective quantum field theories |
| 81U20 | \(S\)-matrix theory, etc. in quantum theory |
| 83C45 | Quantization of the gravitational field |
| 83C27 | Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory |
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