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AdS black holes, the bulk-boundary dictionary, and smearing functions

Leichenauer, Stefan and Rosenhaus, Vladimir (2013) AdS black holes, the bulk-boundary dictionary, and smearing functions. Physical Review D, 88 (2). Art. No. 026003 . ISSN 2470-0010. doi:10.1103/PhysRevD.88.026003.

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In Lorentzian AdS/CFT there exists a mapping between local bulk operators and nonlocal conformal field theory (CFT) operators. In global anti-de Sitter (AdS) this mapping can be found through use of bulk equations of motion and allows the nonlocal CFT operator to be expressed as a local operator smeared over a range of positions and times. We argue that such a construction is not possible if there are bulk normal modes with exponentially small near boundary imprint. We show that the AdS-Schwarzschild background is such a case, with the horizon introducing modes with angular momentum much larger than frequency, causing them to be trapped by the centrifugal barrier. More generally, we argue that any barrier in the radial effective potential which prevents null geodesics from reaching the boundary will lead to modes with vanishingly small near boundary imprint, thereby obstructing the existence of a smearing function. While one may have thought the bulk-boundary dictionary for low curvature regions, such as the exterior of a black hole, should be as in empty AdS, our results demonstrate otherwise.

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Additional Information:© 2013 American Physical Society. Received 23 May 2013; published 8 July 2013. We are grateful to Raphael Bousso and Ben Freivogel for many discussions and insights. We thank Steve Giddings, Don Marolf, Lenny Susskind, Claire Zukowski, and especially Douglas Stanford for helpful discussions. The work of V. R. is supported by the Berkeley Center for Theoretical Physics and NSF GRF. The work of S. L. is supported by a John A. McCone Postdoctoral Fellowship, the U.S. Department of Energy under Contract No. DE-FG02-92ER40701, and the Gordon and Betty Moore Foundation through Grant No. 776 to the Caltech Moore Center for Theoretical Cosmology and Physics.
Group:Caltech Theory, Moore Center for Theoretical Cosmology and Physics
Funding AgencyGrant Number
Berkeley Center for Theoretical PhysicsUNSPECIFIED
John A. McCone Postdoctoral FellowshipUNSPECIFIED
Department of Energy (DOE)DE-FG02-92ER40701
Gordon and Betty Moore Foundation776
Caltech Moore Center for Theoretical Cosmology and PhysicsUNSPECIFIED
Issue or Number:2
Classification Code:PACS: 11.25.Tq
Record Number:CaltechAUTHORS:20130815-083401045
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:39935
Deposited By: Tony Diaz
Deposited On:16 Aug 2013 22:02
Last Modified:09 Nov 2021 23:48

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