Holography at finite N: breakdown of bulk reconstruction for subregions

[摘要] Within AdS/CFT, focusing on the AdS-Rindler wedge, we show that when N is large but finite, correlation functions of reconstructed bulk operators grow exponentially with bulk momentum, overwhelming the usual 1/N suppression. The growth starts when the smeared operator’s ultraviolet scale goes beyond a critical value Λcrit=2πlnN\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ {\Lambda}_{\mathrm{crit}}=\frac{2}{\pi}\ln N $$\end{document}, which is far below the Planck scale. Above this logarithmic threshold, the large N expansion ceases to be reliable, and the would-be bulk operators cannot be consistently defined as observables in the full quantum gravity theory. Since the AdS-Rindler wedge describes the near-horizon region of black holes, this result implies a sharp ln N cutoff for reconstructing bulk operators across horizons. This has a direct impact on whether and how information from the black hole interior is encoded — a central question in the black hole information paradox.

[发布日期] 2026-08-03

[关键词] N;AdS-CFT Correspondence;Gauge-Gravity Correspondence;Black Holes