Holography at Finite N: Breakdown of Bulk Reconstruction for Subregions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916901575196672 |
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| author | Terashima, Seiji |
| author_facet | Terashima, Seiji |
| contents | 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 $Λ_{crit} = \frac{2}π\ln N$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_11592 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Holography at Finite N: Breakdown of Bulk Reconstruction for Subregions Terashima, Seiji High Energy Physics - Theory 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 $Λ_{crit} = \frac{2}π\ln N$, 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. |
| title | Holography at Finite N: Breakdown of Bulk Reconstruction for Subregions |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2508.11592 |