The analytic bootstrap and AdS superhorizon locality - Fitzpatrick, A. Liam; Kaplan, Jared; Poland, David; Simmons-Duffin, David (The journal of high energy physics, 2013)
A bstract 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 | ≪ | υ | < 1. We prove that every CFT with a scalar operator ϕ must contain infinite sequences of operators with twist approaching τ → 2Δ ϕ + 2 n for each integer n as ℓ → ∞. 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 ℓ → ∞. We interpret these results as a statement about superhorizon locality in AdS for general CFTs.