Holography at Finite N: Breakdown of Bulk Reconstruction for Subregions

TL;DR

This paper demonstrates that at finite N, bulk reconstruction in AdS/CFT near black hole horizons breaks down beyond a certain scale, challenging the reliability of bulk operators and impacting black hole information encoding.

Contribution

It reveals a logarithmic cutoff scale for bulk operator reconstruction at finite N, showing the limitations of the large N expansion near horizons.

Findings

Correlation functions grow exponentially with momentum beyond a critical scale

The large N expansion becomes unreliable above the  N scale

Bulk operators cannot be defined as observables beyond the cutoff

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.