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Locality of Gravitational Systems from Entanglement of Conformal Field Theories

Lin, Jennifer and Marcolli, Matilde and Ooguri, Hirosi and Stoica, Bogdan (2015) Locality of Gravitational Systems from Entanglement of Conformal Field Theories. Physical Review Letters, 114 (22). Art. No. 221601. ISSN 0031-9007. doi:10.1103/PhysRevLett.114.221601.

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The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of a minimal surface in its holographic dual. We show that this relation can be inverted for any state in the conformal field theory to compute the bulk stress-energy tensor near the boundary of the bulk spacetime, reconstructing the local data in the bulk from the entanglement on the boundary. We also show that positivity, monotonicity, and convexity of the relative entropy for small spherical domains between the reduced density matrices of any state and of the ground state of the conformal field theory are guaranteed by positivity conditions on the bulk matter energy density. As positivity and monotonicity of the relative entropy are general properties of quantum systems, this can be interpreted as a derivation of bulk energy conditions in any holographic system for which the Ryu-Takayanagi prescription applies. We discuss an information theoretical interpretation of the convexity in terms of the Fisher metric.

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Ooguri, Hirosi0000-0001-6021-3778
Alternate Title:Tomography from Entanglement
Additional Information:© 2015 American Physical Society. Received 27 December 2014; published 2 June 2015. We thank N. Bao, D. Gaiotto, D. Harlow, T. Hartman, P. Hayden, N. Hunter-Jones, C. Keller, D. Kutasov, H. Liu, Y. Nakayama, S. Pufu, P. Sulkowski, T. Takayanagi, M. Van Raamsdonk, and E. Witten for useful discussion. J. L. acknowledges support from the Sidney Bloomenthal fellowship at the University of Chicago. M. M. is currently supported by NSF Grants No. PHY-1205440, No. DMS-1201512, and No. DMS-1007207. H. O. and B. S. are supported in part by the Walter Burke Institute for Theoretical Physics at Caltech, by U.S. DOE Grant No. DE-SC0011632, and by a Simons Investigator award. The work of H. O. is also supported in part by the WPI Initiative of MEXT of Japan and JSPS Grant-in Aid for Scientific Research C-26400240. He also thanks the hospitality of the Aspen Center for Physics and the National Science Foundation, which supports the Center under Grant No. PHY-1066293. B. S. is supported in part by a Dominic Orr Graduate Fellowship. J. L., H. O., and B. S. would like to thank the Institute for Advanced Study, Princeton University, and the Simons Center for Geometry and Physics for hospitality. J. L. also thanks Caltech for hospitality.
Group:Walter Burke Institute for Theoretical Physics
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University of ChicagoUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Ministry of Education, Culture, Sports, Science and Technology (MEXT)UNSPECIFIED
Japan Society for the Promotion of Science (JSPS)C-26400240
Dominic Orr Graduate FellowshipUNSPECIFIED
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Issue or Number:22
Classification Code:PACS numbers: 11.25.Tq
Record Number:CaltechAUTHORS:20150616-152928658
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:58294
Deposited By: Joy Painter
Deposited On:16 Jun 2015 23:19
Last Modified:10 Nov 2021 22:02

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