Local bulk S-matrix elements and CFT singularities

TL;DR

This paper presents a method to derive bulk S-matrix elements from boundary correlators in the AdS/CFT correspondence, using the plane wave limit and boundary sources, with a focus on singular behaviors of Lorentzian correlators.

Contribution

It introduces a procedure to extract bulk S-matrix elements from boundary CFT correlators, validating the approach with supergravity examples and providing a test for holographic duality.

Findings

Successfully reproduces bulk S-matrix elements from boundary correlators.

Identifies specific singular behaviors in Lorentzian correlators crucial for the extraction.

Provides a prescription to test if a boundary CFT can encode bulk physics.

Abstract

We give a procedure for deriving certain bulk S-matrix elements from corresponding boundary correlators. These are computed in the plane wave limit, via an explicit construction of certain boundary sources that give bulk wavepackets. A critical role is played by a specific singular behavior of the lorentzian boundary correlators. It is shown in examples how correlators derived from the bulk supergravity exhibit the appropriate singular structure, and reproduce the corresponding S-matrix elements. This construction thus provides a nontrivial test for whether a given boundary conformal field theory can reproduce bulk physics, and where it does, supplies a prescription to extract bulk S-matrix elements in the plane wave limit.