Holographic cameras: an eye for the bulk

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.

Automated summary

We investigated four-point correlators in an excited quantum state of a field theory and found that a Fourier transform can produce high-quality images of point-like bulk particles in holographic theories. The images reveal the geometry of their movement. For translation-invariant states, the bulk Einstein's equations can be described as local differential equations on correlator data. In non-holographic theories or states, the images are too blurry to extract bulk geometry. We confirmed this by applying formulas from conformal Regge theory to gauge theories at different couplings and the 3D Ising model.