Extracting spacetimes using the AdS/CFT conjecture

TL;DR

This paper develops analytical methods to reconstruct bulk geometries in AdS spacetimes from boundary CFT data, specifically using correlators and entanglement entropy to infer geodesic structures.

Contribution

It introduces new analytical techniques for extracting bulk geometries from boundary data in the AdS/CFT framework, including cases without null circular orbits.

Findings

Static spherically symmetric, asymptotically AdS spacetimes without null circular orbits can be fully recovered.

Any spacetime can be reconstructed up to the local maximum of the potential.

Methods are verified through analytical and numerical examples.

Abstract

We present analytic methods for extracting a class of bulk geometries given information of certain physical quantities in the boundary CFT. More specifically we look at singular correlators and entanglement entropy in the CFT to provide information of null and spacelike geodesics repectively in the bulk. We show that static spherically symmetric, asymptotically AdS spacetimes which do not admit null circular orbits can be fully recovered, and that any spacetime can be recovered up to the local maximum of the potential. We provide analytical and numerical examples to verify the methods used.