Bulk reconstruction using timelike entanglement in (A)dS

Abstract

It is well-known that the entanglement entropies for spacelike subregions, and the associated modular Hamiltonians play a crucial role in the bulk reconstruction program within Anti de-Sitter (AdS) holography. Explicit examples of HKLL map exist mostly for the cases where the emergent bulk region is the so-called entanglement wedge of the given boundary subregion. However, motivated from the complex pseudo-entropy in Euclidean conformal field theories (CFT), one can talk about a `timelike entanglement' in Lorentzian CFTs dual to AdS spacetimes. One can then utilize this boundary timelike entanglement to define a boundary `timelike modular Hamiltonian'. We use constraints involving these Hamiltonians in a manner similar to how it was used for spacelike cases, and write down bulk operators in regions which are not probed by an RT surface corresponding to a single CFT. In the context of two dimensional CFT, we re-derive the HKLL formulas for free bulk scalar fields in three examples: in AdS Poincaré patch, inside and outside of the AdS black hole, and for de Sitter flat slicings. In this method, one no longer requires the knowledge of bulk dynamics for sub-horizon holography.

arXiv commentVersion 2. 51 pages, 13 figures. Minor modifications and corrections. References added. Version 3. Minor changes in abstract and elsewhere. Published version

References in corpus (41)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• The Black Hole in Three Dimensional Space Time
• Eternal Black Holes in AdS
• Towards a derivation of holographic entanglement entropy
• Time Evolution of Entanglement Entropy from Black Hole Interiors
• Notes on Some Entanglement Properties of Quantum Field Theory
• Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
• Relative entropy equals bulk relative entropy
• Holographic representation of local bulk operators
• Bulk vs. Boundary Dynamics in Anti-de Sitter Spacetime
• Holographic Entanglement Entropy
• The Black Hole Singularity in AdS/CFT
• Local bulk operators in AdS/CFT: a boundary view of horizons and locality
• Entanglement Temperature and Entanglement Entropy of Excited States
• Entanglement hamiltonians in two-dimensional conformal field theory
• Bulk locality from modular flow
• Local bulk operators in AdS/CFT: A holographic description of the black hole interior
• Bulk and Boundary Dynamics in BTZ Black Holes
• Holographic Pseudo Entropy
• Entanglement, Holography and Causal Diamonds
• Pseudo Entropy in dS/CFT and Time-like Entanglement Entropy
• Timelike entanglement entropy
• Holographic representation of bulk fields with spin in AdS/CFT
• de Sitter space, extremal surfaces and "time-entanglement"
• A modular toolkit for bulk reconstruction
• Local bulk physics from intersecting modular Hamiltonians
• On holographic time-like entanglement entropy
• Study of the ${\psi }_2(3823)$ and ${\chi }_{c1}(3872)$ states in $B^{+}\to \left(J\psi {\pi }^{+}{\pi }^{-}\right)K^{+}$ decays
• A Modular Sewing Kit for Entanglement Wedges
• Holographic Representation of Higher Spin Gauge Fields
• Modular Flow of Excited States
• Bulk metric reconstruction from boundary entanglement
• Holographic Representation of Local Operators In De Sitter Space
• Fix the dual geometries of $T\bar{T}$ deformed CFT${}_2$ and highly excited states of CFT${}_2$
• Emergence of spacetime from the algebra of total modular Hamiltonians
• Hologram of a pure state black hole
• (A)dS Holography with a Cut-off
• Bulk Reconstruction Beyond the Entanglement Wedge
• Explicit reconstruction of the entanglement wedge
• HKLL for the Non-Normalizable Mode
• Spectrum of Modular Hamiltonian in the Vacuum and Excited States

Cited by in corpus (4)

• Relation between time- and spacelike entanglement entropy
• $dS$ extremal surfaces, replicas, boundary Renyi entropies in $dS/CFT$ and time entanglement
• Horizon causality from holographic scattering in asymptotically dS${}_3$
• Holographic timelike entanglement in AdS${}_3$ Vaidya