We provide a procedure to determine if a given nonlocal operator in a large-$N$ holographic CFT is dual to a local bulk operator on the geometry associated with a particular code subspace of the CFT. This procedure does not presuppose knowledge of the bulk geometry. We are able to pick out local operators in a large region of the bulk, called the “localizable region,” that can extend beyond event horizons in certain cases. The method relies heavily on the quantum error correcting structure of $\mathrm{AdS}/\mathrm{CFT}$ and, in particular, on entanglement wedge reconstruction. As a byproduct of this machinery, we are able to reconstruct the metric in the localizable region up to a conformal factor. This suggests a connection between our program and the recent light-cone cut approach to bulk reconstruction.

• Received 25 April 2017

DOI:https://doi.org/10.1103/PhysRevD.96.026004