Integral geometry and holography
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Publication:2636039
DOI10.1007/JHEP10(2015)175zbMATH Open1388.83217arXiv1505.05515MaRDI QIDQ2636039
Author name not available (Why is that?)
Publication date: 31 May 2018
Published in: (Search for Journal in Brave)
Abstract: We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS/CFT correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS whose kinematic space is two-dimensional de Sitter space.
Full work available at URL: https://arxiv.org/abs/1505.05515
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