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- W4297034812 abstract "We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS$_3$/CFT$_2$ 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$_3$ whose kinematic space is two-dimensional de Sitter space." @default.
- W4297034812 created "2022-09-25" @default.
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- W4297034812 date "2015-05-20" @default.
- W4297034812 modified "2023-10-14" @default.
- W4297034812 title "Integral Geometry and Holography" @default.
- W4297034812 doi "https://doi.org/10.48550/arxiv.1505.05515" @default.
- W4297034812 hasPublicationYear "2015" @default.
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