Reconstructing AdS/CFT

Abstract

In this note we clarify the dictionary between pure quantum gravity on the bulk in the presence of a cosmological constant and a CFT on the boundary. We show for instance that there is a general correspondence between quantum gravity ``radial states'' and a pair of CFT's. Restricting to one CFT is argued to correspond to states possessing an asymptotic infinity. This point of view allows us to address the problem of reconstructing the bulk from the boundary. And in the second part of this paper we present an explicit formula which gives, from the partition function of any 2 dimensional conformal field theory, a wave functional solution to the 3-dimensional Wheeler-DeWitt equation. This establishes at the quantum level a precise dictionary between 2d CFT and pure gravity.

34 pages

References in corpus (17)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• The Holographic Weyl anomaly
• The dS/CFT Correspondence
• Surface Terms as Counterterms in the AdS/CFT Correspondence
• On the Holographic Renormalization Group
• The Holographic Bound in Anti-de Sitter Space
• Quantum Gravity Partition Functions in Three Dimensions
• Three-Dimensional Gravity Revisited
• Mass, Entropy and Holography in Asymptotically de Sitter Spaces
• Supersymmetric Gauge Theories and the AdS/CFT Correspondence
• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
• Holographic Renormalization and Ward Identities with the Hamilton-Jacobi Method
• AdS/CFT correspondence and Geometry
• Is the gravitational action additive?
• Black Hole Thermodynamics and Riemann Surfaces
• Order 1/N^2 test of the Maldacena conjecture: Cancellation of the one-loop Weyl anomaly
• Quantum Effective Action in Spacetimes with Branes and Boundaries: Diffeomorphism Invariance

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• Moving the CFT into the bulk with $T\bar{T}$
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• Quasi-local holographic dualities in non-perturbative 3d quantum gravity I - Convergence of multiple approaches and examples of Ponzano-Regge statistical duals
• Gravitational path integral from the $T^2$ deformation
• Geometrizing $T\bar{T}$
• The strange equation of quantum gravity
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity II - From coherent quantum boundaries to BMS3 characters
• An elementary introduction to loop quantum gravity
• Observations in Quantum Cosmology
• Two dimensional Nearly de Sitter gravity
• A perspective on the landscape problem
• Conformal Boundary Conditions from Cutoff AdS${}_3$
• On c-theorems in arbitrary dimensions
• Stability of Horava-Lifshitz Black Holes in the Context of AdS/CFT
• Shape dynamics and Mach's principles: Gravity from conformal geometrodynamics
• A note on quantum supergravity and AdS/CFT
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• On some (integrable) structures in low-dimensional holography
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• Cost of holographic path integrals
• 3-dimensional $\Lambda$-BMS Symmetry and its Deformations