Puzzles and pitfalls involving Haar-typicality in holography

2017/08/31 by Ning Bao, Aidan Chatwin-Davies
Mathematics · Physics and Astronomy · #Artificial intelligence #Black Holes and Theoretical Physics #Computer science #Cosmology and Gravitation Theories #Dual (grammatical number) #Geometry #Haar #Holography #Linguistics #Mathematics #Noncommutative and Quantum Gravity Theories #Optics #Philosophy #Physics #Point (geometry) #Statistical physics #Theoretical physics #gr-qc #hep-th #quant-ph

paper · pdf · doi:10.21468/scipostphys.4.6.033

published as SciPost Phys. 4, 033 (2018) · 8 pages, v2 fixed formatting in title/abstract, v3 updated page style, v4 reply to SciPost referee report 1 2018-2-8; v5 reply to SciPost referee reports 2 and 3, editor-requested revisions

arxiv created 2018/05/23 · openalex publication_date 2018/06/19 · arxiv updated 2018/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Holographic states that have a well-defined geometric dual in AdS/CFT are not faithfully represented by Haar-typical states in finite-dimensional models. As such, trying to apply principles and lessons from Haar-random ensembles of states to holographic states can lead to apparent puzzles and contradictions. We point out a handful of these pitfalls.

Citations

• Typical event horizons in AdS/CFT
• Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory
• Average entropy of a subsystem
• Particle creation by black holes
• Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
• The Stretched Horizon and Black Hole Complementarity
• Exact holographic mapping and emergent space-time geometry
• The Large-N Limit of Superconformal Field Theories and Supergravity
• Quantum Shannon Theory
• The Black Hole Information Problem
• Moving the CFT into the bulk with T T
• Holographic Entropy Cone Measures