Looking at bulk points in general geometries

TL;DR

This paper explores how boundary correlation functions in holographic duals reveal bulk geometry through sharp features linked to flat-space scattering, providing insights into emergent spacetime in strongly coupled quantum systems.

Contribution

It derives a factorization formula connecting boundary correlators to bulk scattering processes, revealing geometric information from boundary data in holographic states.

Findings

Boundary correlators develop sharp features at bulk points.

Features are controlled by flat-space-like scattering processes.

Boundary hyperboloids encode bulk geometric information.

Abstract

The holographic correspondence predicts that certain strongly coupled quantum systems describe an emergent, higher-dimensional bulk spacetime in which excitations enjoy local dynamics. We consider a general holographic state dual to an asymptotically AdS bulk spacetime, and study boundary correlation functions of local fields integrated against wavepackets. We derive a factorization formula showing that when the wavepackets suitably meet at a common bulk point, the boundary correlators develop sharp features controlled by flat-space-like bulk scattering processes. These features extend along boundary hyperboloids whose shape naturally reveals the bulk geometry. We discuss different choices of operator ordering, which lead to inclusive and out-of-time-ordered amplitudes, as well as fields of various spins and masses.