Holographic geometry/real-space entanglement correspondence and metric reconstruction

Abstract

In holography, the boundary entanglement structure is believed to be encoded in the bulk geometry. In this work, we investigate the precise correspondence between the boundary real-space entanglement and the bulk geometry. By the boundary real-space entanglement, we refer to the conditional mutual information (CMI) for two infinitesimal subsystems separated by a distance $l$, and the corresponding bulk geometry is at a radial position $z_{\ast }$, namely the turning point of the entanglement wedge for a boundary region with a length scale $l$. In a generic geometry described by a given coordinate system, $z_{\ast }$ can be determined locally by $l$, while the exact expression for $z_{\ast }(l)$ depends on the gauge choice, reflecting the inherent nonlocality of this seemingly local correspondence. We propose to specify the function $z_{\ast }(l)$ as the criterion for a gauge choice, and with the specified gauge function, we verify the exact correspondence between the boundary real-space entanglement and the bulk geometry. Inspired by this correspondence, we propose a new method of bulk metric reconstruction from boundary entanglement data, namely the CMI reconstruction. In this CMI proposal, with the gauge fixed a priori by specifying $z_{\ast }(l)$, the bulk metric can be reconstructed from the relation between the bulk geometry and the boundary CMI. The CMI reconstruction method establishes a connection between the differential entropy prescription and Bilson's general algorithm for metric reconstruction.

31 pages, 12 figures; Matching with the published version

References in corpus (19)

• Causality & holographic entanglement entropy
• Holographic Holes in Higher Dimensions
• Holographic Holes and Differential Entropy
• Nuts and Bolts for Creating Space
• Holographic Reconstruction of General Bulk Surfaces
• Extracting the bulk metric from boundary information in asymptotically AdS spacetimes
• Entanglement Wedges for Gravitating Regions
• Extracting Spacetimes using the AdS/CFT Conjecture: Part II
• Entangled Dilaton Dyons
• Covariant Residual Entropy
• Numerical metric extraction in AdS/CFT
• Deep learning bulk spacetime from boundary optical conductivity
• Holographic cameras: an eye for the bulk
• Holographic reconstruction of black hole spacetime: machine learning and entanglement entropy
• Disentangling the gravity dual of Yang-Mills theory
• Dual Geometry of Entanglement Entropy via Deep Learning
• More on the upper bound of holographic n-partite information
• Reconstructing black hole exteriors and interiors using entanglement and complexity
• Entanglement structures from modified IR geometry

Cited by in corpus (1)

• Holographic multipartite entanglement structures in IR modified geometries