Year: 2013
Type: article
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.
Authors: Stefan Leichenauer, Vladimir Rosenhaus
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2057621962