Integral geometry and holographyReport as inadecuate

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Journal of High Energy Physics

, 2015:175

First Online: 27 October 2015Received: 14 August 2015Accepted: 01 October 2015Abstract

We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3-CFT2 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 AdS3 whose kinematic space is two-dimensional de Sitter space.

KeywordsGauge-gravity correspondence AdS-CFT Correspondence ArXiv ePrint: 1505.05515

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Author: Bartłomiej Czech - Lampros Lamprou - Samuel McCandlish - James Sully



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