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Published May 2000 | Submitted + Published
Journal Article Open

Consistency conditions for holographic duality

Abstract

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.

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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August 21, 2023
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