The analytic bootstrap and AdS superhorizon locality

• Published in: The journal of high energy physics Vol. 2013; no. 12; pp. 1 - 35
• Main Authors: Fitzpatrick, A. Liam, Kaplan, Jared, Poland, David, Simmons-Duffin, David
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2013; Springer Nature B.V
• Subjects: Classical and Quantum Gravitation; Coefficients; Correlators; Elementary Particles; High energy physics; Mathematical analysis; Operators; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; Scalars; String Theory; Three dimensional models; Two dimensional; AdS-CFT Correspondence; Nonperturbative Effects; Conformal and W Symmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP12(2013)004

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.