More on Holographic Volumes, Entanglement, and Complexity

2017/09/29 by Dean Carmi, Carmi, Dean
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #Geometric Analysis and Curvature Flows #High Energy Physics - Theory (hep-th)

paper · pdf · doi:10.48550/arxiv.1709.10463

openalex publication_date 2017/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by the holographic prescriptions for computing entanglement entropy and complexity, we study the properties of volumes/areas of bulk surfaces. We obtain a simple formula for the shape dependence of holographic entanglement entropy in terms of a certain integral over the entangling surface. This easily generalizes to any bulk codimension-p extremal surface. We study additional properties of bulk codimension-p extremal surfaces corresponding to strip/plane "entangling surfaces" in various geometries. We compute universal terms for codim-one volumes (conjectured to be dual to holographic subregion complexity) arising from performing relevant deformations. Finally, we describe several interesting bulk surface constructions which are presumably related to holographic complexity.

Citations

• Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
• Computational complexity and black hole horizons
• Complexity Equals Action

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