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Title: Geometries from field theories
Authors: Aoki, Sinya
Kikuchi, Kengo
Onogi, Tetsuya
Author's alias: 青木, 愼也
Issue Date: Oct-2015
Publisher: Oxford University Press (OUP)
Journal title: Progress of Theoretical and Experimental Physics
Volume: 2015
Issue: 10
Thesis number: 101B01
Abstract: We propose a method to define a d+1d+1-dimensional geometry from a dd-dimensional quantum field theory in the 1/N1/N expansion. We first construct a d+1d+1-dimensional field theory from the dd-dimensional one via the gradient-flow equation, whose flow time tt represents the energy scale of the system such that t→0t→0 corresponds to the ultraviolet and t→∞t→∞ to the infrared. We then define the induced metric from d+1d+1-dimensional field operators. We show that the metric defined in this way becomes classical in the large-NN limit, in the sense that quantum fluctuations of the metric are suppressed as 1/N1/N due to the large-NN factorization property. As a concrete example, we apply our method to the O(N)O(N) nonlinear σσ model in two dimensions. We calculate the 3D induced metric, which is shown to describe an anti-de Sitter space in the massless limit. Finally, we discuss several open issues for future studies.
Rights: © The Author(s) 2015. 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 (, which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. Funded by SCOAP3
DOI(Published Version): 10.1093/ptep/ptv131
Appears in Collections:Journal Articles

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