What’s the point? Hole-ography in Poincaré AdS

In the context of the AdS/CFT correspondence, we study bulk reconstruction of the Poincaré wedge of AdS 3 via hole-ography, i.e., in terms of differential entropy of the dual CFT 2 . Previous work had considered the reconstruction of closed or open spacelike curves in global AdS, and of infinitely e...

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Bibliographic Details
Published in:The European physical journal. C, Particles and fields Particles and fields, 2018, Vol.78 (1), p.1-25, Article 75
Main Authors: Espíndola, Ricardo, Güijosa, Alberto, Landetta, Alberto, Pedraza, Juan F.
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics and Cosmology
Construction standards
Elementary Particles
Geodesy
Hadrons
Heavy Ions
Measurement Science and Instrumentation
Nuclear Energy
Nuclear Physics
Periodic variations
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Reconstruction
Regular Article - Theoretical Physics
Segments
String Theory
Wedges
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Summary:In the context of the AdS/CFT correspondence, we study bulk reconstruction of the Poincaré wedge of AdS 3 via hole-ography, i.e., in terms of differential entropy of the dual CFT 2 . Previous work had considered the reconstruction of closed or open spacelike curves in global AdS, and of infinitely extended spacelike curves in Poincaré AdS that are subject to a periodicity condition at infinity. Working first at constant time, we find that a closed curve in Poincaré is described in the CFT by a family of intervals that covers the spatial axis at least twice. We also show how to reconstruct open curves, points and distances, and obtain a CFT action whose extremization leads to bulk points. We then generalize all of these results to the case of curves that vary in time, and discover that generic curves have segments that cannot be reconstructed using the standard hole-ographic construction. This happens because, for the nonreconstructible segments, the tangent geodesics fail to be fully contained within the Poincaré wedge. We show that a previously discovered variant of the hole-ographic method allows us to overcome this challenge, by reorienting the geodesics touching the bulk curve to ensure that they all remain within the wedge. Our conclusion is that all spacelike curves in Poincaré AdS can be completely reconstructed with CFT data, and each curve has in fact an infinite number of representations within the CFT.
ISSN:1434-6044
1434-6052
DOI:10.1140/epjc/s10052-018-5563-0