# The Boundary Dual of Bulk Local Operators

## TL;DR

This paper introduces a procedure to identify whether nonlocal operators in a large N holographic CFT correspond to local bulk operators, leveraging quantum error correction and entanglement wedge reconstruction, and enabling metric reconstruction up to a conformal factor.

## Contribution

The authors develop a bulk reconstruction method that determines local operators without prior bulk geometry knowledge, extending to regions beyond horizons and connecting to light-cone cut techniques.

## Key findings

- Identified a way to determine bulk locality of CFT operators.
- Reconstructed the bulk metric up to a conformal factor.
- Extended the localizable region beyond event horizons.

## Abstract

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 AdS/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.