The Boundary Dual of Bulk Local Operators

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.

16 pages, 7 figures; v2: 18 pages, 7 figures, corrections and clarifications (conclusions unchanged), references added

References in corpus (16)

• Holography from Conformal Field Theory
• Holographic representation of local bulk operators
• Causality & holographic entanglement entropy
• Deriving covariant holographic entanglement
• Constructing local bulk observables in interacting AdS/CFT
• Entwinement and the emergence of spacetime
• Local bulk S-matrix elements and CFT singularities
• Observables, gravitational dressing, and obstructions to locality and subsystems
• Holographic Holes and Differential Entropy
• Nuts and Bolts for Creating Space
• Black Holes, AdS, and CFTs
• Quantum Error Correction of Observables
• Holographic Reconstruction of General Bulk Surfaces
• The Black Hole Interior in Quantum Gravity
• Into the Bulk: A Covariant Approach
• Causal Density Matrices

Cited by in corpus (12)

• Bulk locality from modular flow
• Entanglement Wedge Reconstruction and Entanglement of Purification
• Pulling the Boundary into the Bulk
• Spacetime from Unentanglement
• Bulk metric reconstruction from boundary entanglement
• De Finetti theorems and entanglement in large-N theories and gravity
• Holographic Reconstruction of Bubbles
• Classical Spacetimes as Amplified Information in Holographic Quantum Theories
• Holography in de Sitter and anti-de Sitter Spaces and Gel'fand Graev Radon transform
• Modular Hamiltonians and large diffeomorphisms in $Ad{S}_3$
• Bulk reconstruction in AdS and Gel'fand-Graev-Radon Transform
• Caustics bounding entanglement wedges