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Light-sheets and AdS/CFT

Bousso, Raphael and Leichenauer, Stefan and Rosenhaus, Vladimir (2012) Light-sheets and AdS/CFT. Physical Review D, 86 (4). Art. No. 046009. ISSN 0556-2821. http://resolver.caltech.edu/CaltechAUTHORS:20121008-140830753

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Abstract

One may ask whether the conformal field theory (CFT) restricted to a subset b of the anti-de Sitter (AdS) boundary has a well-defined dual restricted to a subset H(b) of the bulk geometry. The Poincaré patch is an example, but more general choices of b can be considered. We propose a geometric construction of H. We argue that H should contain the set C of causal curves with both endpoints on b. Yet H should not reach so far from the boundary that the CFT has insufficient degrees of freedom to describe it. This can be guaranteed by constructing a superset L of H from light-sheets off boundary slices and invoking the covariant entropy bound in the bulk. The simplest covariant choice is L=L^+∩L^-, where L^+ (L^-) is the union of all future-directed (past-directed) light-sheets. We prove that C = L, so the holographic domain is completely determined by our assumptions: H = C = L. In situations where local bulk operators can be constructed on b, H is closely related to the set of bulk points where this construction remains unambiguous under modifications of the CFT Hamiltonian outside of b. Our construction leads to a covariant geometric renormalization-group flow. We comment on the description of black hole interiors and cosmological regions via AdS/CFT.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevD.86.046009 DOIUNSPECIFIED
http://link.aps.org/doi/10.1103/PhysRevD.86.046009PublisherUNSPECIFIED
Additional Information:© 2012 American Physical Society. Received 11 June 2012; published 24 August 2012. We thank N. Arkani-Hamed, T. Banks, B. Freivogel, J. Kaplan, H. Liu, J. Maldacena, D. Marolf, J. Polchinski, E. Rabinovici, S. Shenker, A. Strominger, L. Susskind, and E. Witten for discussions. This work was supported by the Berkeley Center for Theoretical Physics, by the National Science Foundation (Awards No. 0855653 and No. 0756174), by fqxi Grant No. RFP3-1004, and by the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The work of V. R. is supported by an NSF Graduate Fellowship. The work of S. L. is supported by a John A. McCone Postdoctoral Fellowship.
Group:Caltech Theory
Funders:
Funding AgencyGrant Number
Berkeley Center for Theoretical PhysicsUNSPECIFIED
NSF0855653
NSF0756174
fqxi GrantRFP3-1004
Department of Energy (DOE)DE-AC02-05CH11231
NSF Graduate FellowshipUNSPECIFIED
John A. McCone Postdoctoral FellowshipUNSPECIFIED
Classification Code:PACS: 11.25.Tq
Record Number:CaltechAUTHORS:20121008-140830753
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20121008-140830753
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:34758
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:10 Oct 2012 17:02
Last Modified:08 Mar 2013 21:47

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