The Analytic Bootstrap and AdS Superhorizon Locality

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 φ must contain infinite sequences of operators Oτ,` with twist approaching τ → 2∆φ + 2n for each integer n as `→∞. We show how the rate of approach is controlled by the twist and OPE coefficient of the leading twist operator in the φ× φ 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 `→∞. We interpret these results as a statement about superhorizon locality in AdS for general CFTs. ar X iv :1 21 2. 36 16 v2 [ he pth ] 2 4 Ja n 20 13