The Analytic Bootstrap and AdS Superhorizon Locality

Understand

We take an analytic approach to the CFT bootstrap, studying the 4-pt correlators of d > 2 dimensional CFTs in an Eikonal-type limit, where the conformal cross ratios satisfy |u| << |v| < 1.

• We prove that every CFT with a scalar operator \phi must contain infinite sequences of operators O_{\tau,l} with twist approaching \tau -> 2\Delta_\phi + 2n for each integer n as l -> infinity.
• We show how the rate of approach is controlled by the twist and OPE coefficient of the leading twist operator in the \phi x \phi OPE, and we discuss SCFTs and the 3d Ising Model as examples.
• Additionally, we show that the OPE coefficients of other large spin operators appearing in the OPE are bounded as l -> infinity.