Holographic cameras: an eye for the bulk

TL;DR

This paper demonstrates that Fourier transforming four-point correlators in holographic quantum states can produce clear images of bulk particles, revealing the underlying geometry, unlike in non-holographic states where images are blurry.

Contribution

It introduces a method to visualize bulk geometry from boundary correlators using Fourier transforms, applicable to holographic theories and states.

Findings

Four-point correlators encode bulk geometry.

Fourier transform yields high-quality images in holographic states.

Non-holographic states produce blurry images, confirming the method's specificity.

Abstract

We consider four-point correlators in an excited quantum state of a field theory. We show that, when the theory and state are holographic, a judiciously applied Fourier transform produces high-quality images of point-like bulk particles, revealing the geometry in which they move. For translation-invariant states, the bulk Einstein's equations amount to local differential equations on correlator data. In theories or states that are not holographic, images are too blurry to extract a bulk geometry. We verify this for gauge theories at various couplings and the 3D Ising model by adapting formulas from conformal Regge theory.