Nuts and Bolts for Creating Space
arXiv:1409.4473 · doi:10.1103/PhysRevD.90.106005
Abstract
We discuss the way in which field theory quantities assemble the spatial geometry of three-dimensional anti-de Sitter space (AdS3). The field theory ingredients are the entanglement entropies of boundary intervals. A point in AdS3 corresponds to a collection of boundary intervals, which is selected by a variational principle we discuss. Coordinates in AdS3 are integration constants of the resulting equation of motion. We propose a distance function for this collection of points, which obeys the triangle inequality as a consequence of the strong subadditivity of entropy. Our construction correctly reproduces the static slice of AdS3 and the Ryu-Takayanagi relation between geodesics and entanglement entropies. We discuss how these results extend to quotients of AdS3 -- the conical defect and the BTZ geometries. In these cases, the set of entanglement entropies must be supplemented by other field theory quantities, which can carry the information about lengths of non-minimal geodesics.
37 pages plus appendices, 15 figures
References in corpus (64)
- The Large N Limit of Superconformal Field Theories and Supergravity
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- The Black Hole in Three Dimensional Space Time
- Aspects of Holographic Entanglement Entropy
- A Covariant Holographic Entanglement Entropy Proposal
- Geometry of the 2+1 Black Hole
- Eternal Black Holes in AdS
- Cool horizons for entangled black holes
- Building up spacetime with quantum entanglement
- Entanglement Renormalization and Holography
- Complexity and Shock Wave Geometries
- Time Evolution of Entanglement Entropy from Black Hole Interiors
- Holography from Conformal Field Theory
- Holographic representation of local bulk operators
- Gravitation from Entanglement in Holographic CFTs
- Holographic Probes of Anti-de Sitter Spacetimes
- The Gravity Dual of a Density Matrix
- Causality & holographic entanglement entropy
- Gravitational Dynamics From Entanglement "Thermodynamics"
- Remarks on entanglement entropy for gauge fields
- Local bulk operators in AdS/CFT: a boundary view of horizons and locality
- D-branes and Fat Black Holes
- A holographic proof of the strong subadditivity of entanglement entropy
- Holographic Particle Detection
- Correlation functions for M^N/S_N orbifolds
- Decomposition of entanglement entropy in lattice gauge theory
- Inside the Horizon with AdS/CFT
- Constructing local bulk observables in interacting AdS/CFT
- Causal Holographic Information
- On geodesic propagators and black hole holography
- A hole-ographic spacetime
- Entwinement and the emergence of spacetime
- Comments on quantum gravity and entanglement
- Entanglement entropy and nonabelian gauge symmetry
- Holographic entanglement plateaux
- Universality of Gravity from Entanglement
- Physics at the entangling surface
- Massless black holes and black rings as effective geometries of the D1-D5 system
- Rindler Quantum Gravity
- Exact holographic mapping and emergent space-time geometry
- Holographic Holes in Higher Dimensions
- Black Hole Creation in 2+1 Dimensions
- Holographic Holes and Differential Entropy
- A New Approach to String Cosmology
- Light-sheets and AdS/CFT
- The entropy of a hole in spacetime
- On Spacetime Entanglement
- Multi-matrix models and emergent geometry
- Disk entanglement entropy for a Maxwell field
- Extracting the bulk metric from boundary information in asymptotically AdS spacetimes
- Small AdS black holes from SYM
- Coarse-grained entropy and causal holographic information in AdS/CFT
- Extracting spacetimes using the AdS/CFT conjecture
- Extracting Spacetimes using the AdS/CFT Conjecture: Part II
- Properties of Causal Holographic Information
- Covariant Residual Entropy
- On the Architecture of Spacetime Geometry
- Extremal Surfaces in Asymptotically AdS Charged Boson Stars Backgrounds
- Twistor Theory and Differential Equations
- Constructing Space From Entanglement Entropy
- Deriving the First Law of Black Hole Thermodynamics without Entanglement
- Strong Subadditivity and Emergent Surface
- Holography and entropy bounds in the plane wave matrix model
- A Holographic Approach to Spacetime Entanglement
Cited by in corpus (61)
- Surface/State Correspondence as a Generalized Holography
- Entwinement and the emergence of spacetime
- Bit threads and holographic entanglement
- Entanglement Wedge Cross Section from the Dual Density Matrix
- Geometric Aspects of Holographic Bit Threads
- Entanglement Wedge Reconstruction and Entanglement of Purification
- Holographic Subregion Complexity from Kinematic Space
- Quantum Information in Holographic Duality
- Tomography from Entanglement
- Towards Bulk Metric Reconstruction from Extremal Area Variations
- The Information Theoretic Interpretation of the Length of a Curve
- Towards a Reconstruction of General Bulk Metrics
- Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
- Exploring the Tensor Networks/AdS Correspondence
- Entwinement in discretely gauged theories
- WdW-patches in AdS and complexity change under conformal transformations II
- Constructing AdS_2 flow geometries
- Topological shadows and complexity of islands in multiboundary wormholes
- Bit threads, Einstein's equations and bulk locality
- Entanglement entropy from one-point functions in holographic states
- Holographic reconstruction of black hole spacetime: machine learning and entanglement entropy
- Kinematic space for conical defects
- Gravitational back-reaction is magical
- Covariant Constraints on Hole-ography
- The Boundary Dual of Bulk Local Operators
- Berry phases, wormholes and factorization in AdS/CFT
- Bulk reconstruction of metrics with a compact space asymptotically
- Machine Learning Statistical Gravity from Multi-Region Entanglement Entropy
- Building Bulk Geometry from the Tensor Radon Transform
- More of the Bulk from Extremal Area Variations
- Holographic Coarse-Graining: Correlators from the Entanglement Wedge and Other Reduced Geometries
- Into the Bulk: A Covariant Approach
- Bulk reconstruction of metrics inside black holes by complexity
- Holographic Reconstruction of Bubbles
- Quantum bit threads and holographic entanglement
- Integral Geometry and Holography
- Holographic integral geometry with time dependence
- Entanglement renormalization and integral geometry
- The first law of differential entropy and holographic complexity
- What's the Point? Hole-ography in Poincare AdS
- More on the upper bound of holographic n-partite information
- Thread/State correspondence: from bit threads to qubit threads
- Reconstructing black hole exteriors and interiors using entanglement and complexity
- Losing the IR: a Holographic Framework for Area Theorems
- Reconstruction of an AdS Radiation/Boson Star Bulk Geometry Using Light-cone Cuts
- Emergent geometry, thermal CFT and surface/state correspondence
- Scaling limits of complex Sachdev-Ye-Kitaev models and holographic geometry
- Holographic geometry/real-space entanglement correspondence and metric reconstruction
- Weaving the (AdS) spaces with partial entanglement entropy threads
- Entanglement entropy and kinematic space in BCFT and RG flow
- QCD, with Strings Attached
- Boundary and bulk notions of transport in the AdS/CFT correspondence
- Light-cone cuts and hole-ography: explicit reconstruction of bulk metrics
- Building bulk from Wilson loops
- Holographic Complexity in Charged Accelerating Black Holes
- Illuminating entanglement shadows of BTZ black holes by a generalized entanglement measure
- Bulk reconstruction of AdS metrics and developing kinematic space
- On Emergent Geometry from Entanglement Entropy in Matrix theory
- Conformal Rigidity from Focusing
- Quantum Information Approaches to Quantum Gravity
- A note on the kinematic space associated with a subregion