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Proof of the Holographic Formula for Entanglement Entropy

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arxiv hep-th/0606184 v2 pith:6EYK4GAX submitted 2006-06-20 hep-th cond-mat.otherquant-ph

Dmitri V. Fursaev This is my paper
classification hep-thcond-mat.otherquant-ph
keywords entropyentanglementformulaholographictermsboundarybulkconditions
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Entanglement entropy for a spatial partition of a quantum system is studied in theories which admit a dual description in terms of the anti-de Sitter (AdS) gravity one dimension higher. A general proof of the holographic formula which relates the entropy to the area of a codimension 2 minimal hypersurface embedded in the bulk AdS space is given. The entanglement entropy is determined by a partition function which is defined as a path integral over Riemannian AdS geometries with non-trivial boundary conditions. The topology of the Riemannian spaces puts restrictions on the choice of the minimal hypersurface for a given boundary conditions. The entanglement entropy is also considered in Randall-Sundrum braneworld models where its asymptotic expansion is derived when the curvature radius of the brane is much larger than the AdS radius. Special attention is payed to the geometrical structure of anomalous terms in the entropy in four dimensions. Modification of the holographic formula by the higher curvature terms in the bulk is briefly discussed.

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Cited by 4 Pith papers

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

  1. Temporal Entanglement from Twist Correlators in 2d Conformal Field Theory and Holography

    hep-th 2026-07 conditional novelty 7.0 of 10

    Timelike entanglement entropy in 2d CFT is defined by time-ordered twist correlators, whose holographic saddles are complex geodesics with smallest real length, and whose imaginary part counts causal-diamond crossings...

  2. A revision to the QES prescription

    hep-th 2025-06 reject novelty 6.0 of 10

    The paper proposes a weighted-sum revision of the quantum extremal surface formula, but the weight is assumed rather than derived.

  3. Renormalized pseudoentropy in dS/CFT

    hep-th 2026-02 conditional novelty 5.0 of 10

    Renormalized holographic pseudoentropy in dS/CFT is constructed from conformal-gravity actions in four and six dimensions, yielding finite sphere values and Mezei-like shape dependence for small deformations.

  4. Lectures on entanglement entropy in field theory and holography

    hep-th 2019-07 unverdicted

    Lecture notes surveying entanglement entropy in QFT and holography, emphasizing physical aspects and the Ryu-Takayanagi formula.

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