Explicit reconstruction of the entanglement wedge

Abstract

The problem of how the boundary encodes the bulk in AdS/CFT is still a subject of study today. One of the major issues that needs more elucidation is the problem of subregion duality; what information of the bulk a given boundary subregion encodes. Although the proof given by Dong, Harlow, and Wall states that the entanglement wedge of the bulk should be encoded in boundary subregions, no explicit procedure for reconstructing the entanglement wedge was given so far. In this paper, mode sum approach to obtaining smearing functions for a single bulk scalar is generalised to include bulk reconstruction in the entanglement wedge of boundary subregions. It is generally expectated that solutions to the wave equation on a complicated coordinate patch are needed, but this hard problem has been transferred to a less hard but tractable problem of matrix inversion.

version accepted by JHEP; added references and discussions on covariance

References in corpus (7)

• Holographic representation of local bulk operators
• Constructing local bulk observables in interacting AdS/CFT
• Observables, gravitational dressing, and obstructions to locality and subsystems
• Universality of Gravity from Entanglement
• Holographic Holes and Differential Entropy
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Cited by in corpus (9)

• Cauchy Slice Holography: A New AdS/CFT Dictionary
• Bulk Locality in AdS/CFT Correspondence
• Bulk reconstruction using timelike entanglement in (A)dS
• Holographic Coarse-Graining: Correlators from the Entanglement Wedge and Other Reduced Geometries
• Explicit reconstruction of the entanglement wedge via the Petz map
• Wormholes, geons, and the illusion of the tensor product
• Simple Bulk Reconstruction in AdS/CFT Correspondence
• Symmetry transformation of subregion bulk representations
• Bulk reconstruction and Bogoliubov transformations in AdS${}_2$