Holography from the Wheeler-DeWitt equation

Abstract

In a theory of quantum gravity, states can be represented as wavefunctionals that assign an amplitude to a given configuration of matter fields and the metric on a spatial slice. These wavefunctionals must obey a set of constraints as a consequence of the diffeomorphism invariance of the theory, the most important of which is known as the Wheeler-DeWitt equation. We study these constraints perturbatively by expanding them to leading nontrivial order in Newton's constant about a background AdS spacetime. We show that, even within perturbation theory, any wavefunctional that solves these constraints must have specific correlations between a component of the metric at infinity and energetic excitations of matter fields or transverse-traceless gravitons. These correlations disallow strictly localized excitations. We prove perturbatively that two states or two density matrices that coincide at the boundary for an infinitesimal interval of time must coincide everywhere in the bulk. This analysis establishes a perturbative version of holography for theories of gravity coupled to matter in AdS.

arXiv commentv2: minor clarifications, matches published version, 58 pages, 1 figure

References in corpus (50)

• Gauge Theory Correlators from Non-Critical String Theory
• Large N Field Theories, String Theory and Gravity
• The Dynamics of General Relativity
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• Towards a derivation of holographic entanglement entropy
• The entropy of Hawking radiation
• The Gravitational Hamiltonian, Action, Entropy, and Surface Terms
• Gravitation from Entanglement in Holographic CFTs
• Asymptotically Anti-de Sitter Space-times: Conserved Quantities
• State-Dependent Bulk-Boundary Maps and Black Hole Complementarity
• xPert: Computer algebra for metric perturbation theory
• Exact Dirac Quantization of All 2-D Dilaton Gravity Theories
• Inconsistency of Islands in Theories with Long-Range Gravity
• Stability of Black Holes and Black Branes
• Diffeomorphism-invariant observables and their nonlocal algebra
• Edge modes of gravity -- I: Corner potentials and charges
• Observables for Two-Dimensional Black Holes
• Entanglement entropy and $T\overline{T}$ deformation
• Observables, gravitational dressing, and obstructions to locality and subsystems
• Nonlinear Gravity from Entanglement in Conformal Field Theories
• Defect Conformal Field Theory and Locally Localized Gravity
• Flat-space scattering and bulk locality in the AdS/CFT correspondence
• The Holographic Nature of Null Infinity
• Unitarity and Holography in Gravitational Physics
• Edge modes of gravity -- II: Corner metric and Lorentz charges
• $T\bar{T}$ Deformations, Massive Gravity and Non-Critical Strings
• Sphere partition functions and cut-off AdS
• How is quantum information localized in gravity?
• Moving the CFT into the bulk with $T\bar{T}$
• $T\bar{T}$-Deformed Actions and (1,1) Supersymmetry
• Gravitational dressing, soft charges, and perturbative gravitational splitting
• Asymptotic Flatness, Little String Theory, and Holography
• Reconstructing AdS/CFT
• A toy model of black hole complementarity
• Gravitational splitting at first order: Quantum information localization in gravity
• Boundary unitarity and the black hole information paradox
• Gravitational path integral from the $T^2$ deformation
• Diffeomorphism invariance and the black hole information paradox
• Geometrizing $T\bar{T}$
• Random Boundary Geometry and Gravity Dual of $T\bar{T}$ Deformation
• Kerr-AdS and its Near-horizon Geometry: Perturbations and the Kerr/CFT Correspondence
• Liouville theory and Matrix models: A Wheeler DeWitt perspective
• Introductory Lectures on Quantum Cosmology (1990)
• $T\bar{T}$ deformed YM${}_2$ on general backgrounds from an integral transformation
• Is Holography Implicit in Canonical Gravity?
• A Toy Model of the Information Paradox in Empty Space
• Analytic Solutions of The Wheeler-DeWitt Equation in Spherically Symmetric Space-time
• Exact Solutions to the Wheeler-DeWitt Equation of Two Dimensional Dilaton Gravity
• Wheeler-De Witt equation and AdS/CFT correspondence

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• Inconsistency of Islands in Theories with Long-Range Gravity
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• Cauchy Slice Holography: A New AdS/CFT Dictionary
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• Ephemeral Islands, Plunging Quantum Extremal Surfaces and BCFT channels
• Berry phases, wormholes and factorization in AdS/CFT
• Holographic Coarse-Graining: Correlators from the Entanglement Wedge and Other Reduced Geometries
• On the questions of asymptotic recoverability of information and subsystems in quantum gravity
• Holography of information in massive gravity using Dirac brackets
• A comment on a fine-grained description of evaporating black holes with baby universes
• A "black hole theorem," and its implications
• Perturbative quantum evolution of the gravitational state and dressing in general backgrounds
• Schrödinger evolution of two-dimensional black holes
• Recovering information in an asymptotically flat spacetime in quantum gravity
• Wormholes, geons, and the illusion of the tensor product
• Graviton Mass and Entanglement Islands in Low Spacetime Dimensions
• Euclidean-to-Lorentzian wormhole transition and gravitational symmetry breaking in the Sachdev-Ye-Kitaev model