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The Diagonal Approximation for Holographic R\'{e}nyi Entropies

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arxiv 2412.03670 v1 pith:BPC6KSE4 submitted 2024-12-04 hep-th gr-qcquant-ph

Geoff Penington , Pratik Rath This is my paper · ORCID
classification hep-thgr-qcquant-ph
keywords prescriptionbranecosmicalphaapproximationdiagonalderiveentropies
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abstract

Recently Dong, Rath and Kudler-Flam proposed a modified cosmic brane prescription for computing the R\'{e}nyi entropy $S_\alpha$ of a holographic system in the presence of multiple extremal surfaces. This prescription was found by assuming a diagonal approximation, where the R\'{e}nyi entropy is computed after first measuring the areas of all extremal surfaces. We derive this diagonal approximation and show that it accurately computes R\'{e}nyi entropies up to $O(\log G)$ corrections. For $\alpha<1$, this allows us to derive the modified cosmic brane prescription, which differs from the original cosmic brane prescription at leading order in $G$. For $\alpha>1$, it leads to the original cosmic brane prescription without needing to assume that replica symmetry is unbroken in the bulk.

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Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Universality of Magic in Local Quantum Field Theory

    hep-th 2026-07 conditional novelty 7.0 of 10

    In any local QFT, vacuum-like states have non-flat entanglement spectra because local algebras are type III₁, so no stabilizer state can flow to them in the continuum: QFT states necessarily carry magic.

  2. Hollow-grams: Generalized Entanglement Wedges from the Gravitational Path Integral

    hep-th 2025-06 conditional novelty 7.0 of 10

    The entropy of a bulk region in holographic states equals the generalized entropy of the smallest wedge containing it, derived from a replica path integral via a hollow-graphic construction.

  3. A Reverse Black Hole Information Problem

    hep-th 2026-01 conditional novelty 6.0 of 10

    Exact CFT states for colliding particles that form evaporating AdS black holes are constructed, and several coarse-graining maps are shown to convert the exact pure state into mixed semiclassical Hawking radiation wit...

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