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Published September 27, 2013 | Published + Submitted
Journal Article Open

Null geodesics, local CFT operators, and AdS/CFT for subregions

Abstract

We investigate the nature of the AdS/CFT duality between a subregion of the bulk and its boundary. In global AdS/CFT in the classical G_N=0 limit, the duality reduces to a boundary value problem that can be solved by restricting to one-point functions of local operators in the conformal field theory (CFT). We show that the solution of this boundary value problem depends continuously on the CFT data. In contrast, the anti–de Sitter (AdS)-Rindler subregion cannot be continuously reconstructed from local CFT data restricted to the associated boundary region. Motivated by related results in the mathematics literature, we posit that a continuous bulk reconstruction is only possible when every null geodesic in a given bulk subregion has an endpoint on the associated boundary subregion. This suggests that a subregion duality for AdS-Rindler, if it exists, must involve nonlocal CFT operators in an essential way.

Additional Information

© 2013 American Physical Society. Received 31 May 2013; published 27 September 2013. We are grateful to many of our colleagues for extensive and very helpful discussions over the painful course of this work, especially J. de Boer, V. Hubeny, J. Maldacena, D. Marolf, I. Rodnianski, S. Shenker, L. Susskind, M. van Raamsdonk, and E. Verlinde. This work was supported by the Berkeley Center for Theoretical Physics, by the National Science Foundation (award numbers 0855653 and 0756174), by fqxi Grant No. RFP3-1004, and by the US Department of Energy under Contract No. DE-AC02-05CH11231. The work of V. R. and C. Z. is supported by NSF Graduate Fellowships. The work of S. L. is supported by a John A. McCone Postdoctoral Fellowship.

Attached Files

Published - PhysRevD.88.064057.pdf

Submitted - 1209.4641v1.pdf

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August 23, 2023
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