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Consistency conditions for holographic duality

Balasubramanian, Vijay and Gimon, Eric and Minic, Djordje (2000) Consistency conditions for holographic duality. Journal of High Energy Physics, 2000 (5). Art. No. 014. ISSN 1126-6708. doi:10.1088/1126-6708/2000/05/014.

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We show that if the beta functions of a field theory are given by the gradient of a certain potential on the space of couplings, a gravitational background in one more dimension can express the renormalization group (RG) flow of the theory. The field theory beta functions and the gradient flow constraint together reconstruct the second-order spacetime equations of motion. The RG equation reduces to the conventional gravitational computation of the spacetime quasilocal stress tensor, and a c-theorem holds true as a consequence of the Raychaudhuri equation. Conversely, under certain conditions, if the RG evolution of a field theory possesses a monotonic c-function, the flow of couplings can be expressed in terms of a higher-dimensional gravitational background.

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Additional Information:© 2000 IOP Publishing. Received: April 22, 2000, Accepted: May 4, 2000. We have benefitted from discussions with M. Douglas, P. Hořava, P. Kraus, S. Shenker, E. Verlinde, H. Verlinde, N. Warner, E. Witten, and, particularly, J. de Boer and R. Gopakumar. V.B. was supported by the Harvard Society of Fellows, the Milton Fund of Harvard University, and NSF grant NSF-PHY-9802709. E.G. was supported by DOE grant DE-FG03-92ER40701. D.M. was supported by DOE grant DE-FG03-84ER40168. V.B. is grateful to the University of Chicago and UCLA where part of this work was completed. D.M. enjoyed the hospitality of the University of Illinois at Chicago during this project. Recent work which overlaps with the content of this paper appears in [35].
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Harvard Society of FellowsUNSPECIFIED
Harvard University Milton FundUNSPECIFIED
Department of Energy (DOE)DE-FG03-92ER40701
Department of Energy (DOE)DE-FG03-84ER40168
Subject Keywords:renormalization regularization and renormalons; AdS-CFT correspondance
Issue or Number:5
Classification Code:PACS: 11.10.Hi; 04.50.-h; 04.60.-m
Record Number:CaltechAUTHORS:20111117-094337995
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Official Citation:1.Consistency conditions for holographic duality Vijay Balasubramanian et al JHEP05(2000)014
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27825
Deposited By: Tony Diaz
Deposited On:17 Nov 2011 21:09
Last Modified:09 Nov 2021 16:52

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