A bstract It is a longstanding conjecture that any CFT with a large central charge and a large gap ∆ gap in the spectrum of higherspin singletrace 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 Smatrix dispersion relations in appropriate limits. This dictionary allows us to apply recentlydeveloped flatspace methods to construct positive CFT functionals. We show how AdS 4 naturally resolves the infrared divergences present in 4D flatspace bounds. Our results imply the validity of twicesubtracted dispersion relations for any Smatrix arising from the flatspace limit of AdS/CFT.
Dispersive CFT sum rules
A bstract We give a unified treatment of dispersive sum rules for fourpoint correlators in conformal field theory. We call a sum rule “dispersive” if it has double zeros at all doubletwist operators above a fixed twist gap. Dispersive sum rules have their conceptual origin in Lorentzian kinematics and absorptive physics (the notion of double discontinuity). They have been discussed using three seemingly different methods: analytic functionals dual to doubletwist operators, dispersion relations in position space, and dispersion relations in Mellin space. We show that these three approaches can be mapped into one another and lead to completely equivalent sum rules. A central idea of our discussion is a fully nonperturbative expansion of the correlator as a sum over PolyakovRegge blocks . Unlike the usual OPE sum, the PolyakovRegge expansion utilizes the data of two separate channels, while having (term by term) good Regge behavior in the third channel. We construct sum rules which are nonnegative above the doubletwist gap; they have the physical interpretation of a subtracted version of “superconvergence” sum rules. We expect dispersive sum rules to be a very useful tool to study expansions around meanfield theory, and to constrain the lowenergy description of holographic CFTs with more »
 Award ID(s):
 1915093
 Publication Date:
 NSFPAR ID:
 10249286
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2021
 Issue:
 5
 ISSN:
 10298479
 Sponsoring Org:
 National Science Foundation
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