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Title: AdS geometry from CFT on a general conformally flat manifold
Authors: Aoki, Sinya
Yokoyama, Shuichi
Author's alias: 青木, 愼也
横山, 修一
Issue Date: Aug-2018
Publisher: Elsevier BV
Journal title: Nuclear Physics B
Volume: 933
Start page: 262
End page: 274
Abstract: We construct an anti-de-Sitter (AdS) geometry from a conformal field theory (CFT) defined on a general conformally flat manifold via a flow equation associated with the curved manifold, which we refer to as the primary flow equation. We explicitly show that the induced metric associated with the primary flow equation becomes AdS whose boundary is the curved manifold. Interestingly, it turns out that such an AdS metric with conformally flat boundary is obtained from the usual Poincare AdS by a simple bulk finite diffeomorphism. We also demonstrate that the emergence of such an AdS space is guaranteed only by the conformal symmetry at boundary, which converts to the AdS isometry after quantum averaging, as in the case of the flat boundary. As a side remark we show that a geometry with one warped direction becomes an Einstein manifold if and only if so is its boundary at the warped direction, and briefly discuss a possibility of a little extension beyond AdS/CFT correspondence by using a genuine Einstein geometry.
Rights: © 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.
URI: http://hdl.handle.net/2433/233088
DOI(Published Version): 10.1016/j.nuclphysb.2018.06.004
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