No Ensemble Averaging Below the Black Hole Threshold

Abstract

In the AdS/CFT correspondence, amplitudes associated to connected bulk manifolds with disconnected boundaries have presented a longstanding mystery. A possible interpretation is that they reflect the effects of averaging over an ensemble of boundary theories. But in examples in dimension $D\ge 3$, an appropriate ensemble of boundary theories does not exist. Here we sharpen the puzzle by identifying a class of "sub-threshold" observables that we claim do not show effects of ensemble averaging. These are amplitudes that do not involve black hole states. To support our claim, we explore the example of $D=3$, and show that connected solutions of Einstein's equations with disconnected boundary never contribute to sub-threshold observables. To demonstrate this requires some novel results about the renormalized volume of a hyperbolic three-manifold, which we prove using modern methods in hyperbolic geometry. Why then do any observables show apparent ensemble averaging? We propose that this reflects the chaotic nature of black hole physics and the fact that the Hilbert space describing a black hole does not have a large $N$ limit.

arXiv comment43pp, clarifications and corrections in v. 2 and some more precise results about volumes, minor corrections in v. 3

References in corpus (19)

• The Large N Limit of Superconformal Field Theories and Supergravity
• The Black Hole in Three Dimensional Space Time
• The Holographic Weyl anomaly
• Eternal Black Holes in AdS
• Black holes and the butterfly effect
• Black Hole Entropy from Near-Horizon Microstates
• Review of AdS/CFT Integrability: An Overview
• Quantum Gravity Partition Functions in Three Dimensions
• Wormholes in AdS
• Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information
• Conformal Anomaly Of Submanifold Observables In AdS/CFT Correspondence
• AdS${}_3$ gravity and random CFT
• The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral
• A new handle on three-point coefficients: OPE asymptotics from genus two modular invariance
• On the renormalized volume of hyperbolic 3-manifolds
• 3D Gravity, Point Particles and Liouville Theory
• Liouville action and Weil-Petersson metric on deformation spaces, global Kleinian reciprocity and holography
• Schwarzian derivatives, projective structures, and the Weil-Petersson gradient flow for renormalized volume
• A symplectic map between hyperbolic and complex Teichmüller theory

Cited by in corpus (16)

• Large N algebras and generalized entropy
• Semiclassical 3D gravity as an average of large-c CFTs
• Harnessing S-Duality in $\mathcal{N}=4$ SYM & Supergravity as $SL(2,\mathbb{Z})$-Averaged Strings
• Gravitational orbits, double-twist mirage, and many-body scars
• Wormholes from heavy operator statistics in AdS/CFT
• Synthetic Fuzzballs: A Linear Ramp from Black Hole Normal Modes
• A precision test of averaging in AdS/CFT
• Combinatoric topological string theories and group theory algorithms
• Vacuum Transitions in Two-Dimensions and their Holographic Interpretation
• Holographic QFTs on AdS${}_d$, wormholes and holographic interfaces
• Quantum evolution of the Hawking state for black holes
• Higher spin JT gravity and a matrix model dual
• (Half) Wormholes under Irrelevant Deformation
• Factorization and global symmetries in holography
• Replicas, averaging and factorization in the IIB matrix model
• A universal sum over topologies in 3d gravity