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Title: Integral geometry and holography

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.
 [1] ;  [1] ;  [1] ;  [2]
  1. Stanford Univ., Stanford, CA (United States)
  2. SLAC National Accelerator Lab., Menlo Park, CA (United States)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 1029-8479; arXiv:1505.05515
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2015; Journal Issue: 10; Journal ID: ISSN 1029-8479
Springer Berlin
Research Org:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; Theory-HEP; HEPTH; gauge-gravity correspondence; AdS-CFT correspondence