Journal of High Energy Physics (Nov 2021)

AdS bulk locality from sharp CFT bounds

  • Simon Caron-Huot,
  • Dalimil Mazáč,
  • Leonardo Rastelli,
  • David Simmons-Duffin

DOI
https://doi.org/10.1007/JHEP11(2021)164
Journal volume & issue
Vol. 2021, no. 11
pp. 1 – 92

Abstract

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Abstract It is a long-standing conjecture that any CFT with a large central charge and a large gap ∆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 ∆gap using the conformal bootstrap. Our bounds exhibit the scaling in ∆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 AdS4 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.

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