The Analytic Bootstrap and AdS Superhorizon Locality

TL;DR

This paper develops an analytic approach to the conformal bootstrap in higher-dimensional CFTs, revealing infinite sequences of operators with predictable twists and bounded OPE coefficients, supporting superhorizon locality in AdS.

Contribution

It introduces an analytic method to study the CFT bootstrap in an Eikonal limit, establishing the behavior of large spin operators and their OPE coefficients, and connects these to AdS superhorizon locality.

Findings

Operators with twist approaching 2Δ_φ + 2n as spin increases

OPE coefficients of large spin operators are bounded

Results support superhorizon locality in AdS for general CFTs

Abstract

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. We interpret these results as a statement about superhorizon locality in AdS for general CFTs.