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arXiv · 2508.11592

Holography at Finite N: Breakdown of Bulk Reconstruction for Subregions

Seiji Terashima
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Abstract

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 $\Lambda_{crit} = \frac{2}{\pi}\ln N$, 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.

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Seiji Terashima. 2025-08-15. Holography at Finite N: Breakdown of Bulk Reconstruction for Subregions. https://arxiv.org/abs/2508.11592

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