# Correlation functions at the bulk point singularity from the gravitational eikonal S-matrix

## TL;DR

This paper explores how the bulk point singularity in conformal correlators reveals local bulk physics in AdS and proposes a map connecting flat space scattering matrices to boundary correlation functions, validated through gravitational scattering examples.

## Contribution

It introduces a new map from flat space S-matrix to conformal correlators at the bulk point singularity, specifically applied to perturbative gravitational scattering.

## Key findings

- The eikonal limit of gravitational scattering maps to a conformal correlator at the bulk point.
- The inverse map recovers previous proposals relating flat space S-matrix to boundary correlators.
- Validation through explicit computation of gravitational scattering in the eikonal limit.

## Abstract

The bulk point singularity limit of conformal correlation functions in Lorentzian signature acts as a microscope to look into local bulk physics in AdS. From it we can extract flat space scattering processes localized in AdS that ultimate should be related to corresponding observables on the conformal field theory at the boundary. In this paper we use this interesting property to propose a map from flat space s-matrix to conformal correlation functions and try it on perturbative gravitational scattering. In particular, we show that the eikonal limit of gravitation scattering maps to a correlation function of the expected form at the bulk point singularity. We also compute the inverse map recovering a previous proposal in the literature.