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Title: Flow equation, conformal symmetry, and anti-de Sitter geometry
Authors: Aoki, Sinya
Yokoyama, Shuichi
Author's alias: 青木, 愼也
Keywords: B21 AdS/CFT correspondence
Issue Date: Mar-2018
Publisher: Oxford University Press (OUP)
Journal title: Progress of Theoretical and Experimental Physics
Volume: 2018
Issue: 3
Thesis number: 031B01
Abstract: We argue that the anti-de Sitter (AdS) geometry in d+1 dimensions naturally emerges from an arbitrary conformal field theory in d dimensions using the free flow equation. We first show that an induced metric defined from the flowed field generally corresponds to the quantum information metric, called the Bures or Helstrom metric, if the flowed field is normalized appropriately. We next verify that the induced metric computed explicitly with the free flow equation always becomes the AdS metric when the theory is conformal. We finally prove that the conformal symmetry in d dimensions converts to the AdS isometry in d+1 dimensions after d-dimensional quantum averaging. This guarantees the emergence of AdS geometry without explicit calculation.
Rights: © The Author(s) 2018. Published by Oxford University Press on behalf of the Physical Society of Japan. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.Funded by SCOAP3.
URI: http://hdl.handle.net/2433/250308
DOI(Published Version): 10.1093/ptep/pty013
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