Integral geometry and holography

Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James

doi:10.1007/JHEP10(2015)175

Title: Integral geometry and holography

Journal Article · Tue Oct 27 00:00:00 EDT 2015 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP10(2015)175· OSTI ID:1183697

Czech, Bartlomiej ^[1]; Lamprou, Lampros ^[1]; McCandlish, Samuel ^[1]; Sully, James ^[2]

Stanford Univ., Stanford, CA (United States)
SLAC National Accelerator Lab., Menlo Park, CA (United States)

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.

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Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: AC02-76SF00515

OSTI ID:: 1183697

Report Number(s):: SLAC-PUB-16293; arXiv:1505.05515

Journal Information:: Journal of High Energy Physics (Online), Vol. 2015, Issue 10; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 127 works

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