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

Stefan Leichenauer and Vladimir Rosenhaus
Phys. Rev. D 88, 026003 – Published 8 July 2013

Abstract

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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  • Received 23 May 2013

DOI:https://doi.org/10.1103/PhysRevD.88.026003

© 2013 American Physical Society

Authors & Affiliations

Stefan Leichenauer1,* and Vladimir Rosenhaus2,†

  • 1California Institute of Technology, Pasadena, California 91125, USA
  • 2Center for Theoretical Physics and Department of Physics, University of California, Berkeley, California 94720, USA

  • *sleichen@theory.caltech.edu
  • vladr@berkeley.edu

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Issue

Vol. 88, Iss. 2 — 15 July 2013

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