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Title: Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT
Authors: Caputa, Pawel
Kundu, Nilay
Miyaji, Masamichi
Takayanagi, Tadashi  kyouindb  KAKEN_id  orcid (unconfirmed)
Watanabe, Kento
Author's alias: 宮地, 真路
髙柳, 匡
Keywords: AdS-CFT Correspondence
Anomalies in Field and String Theories
Conformal Field Theory
Holography and condensed matter physics (AdS/CMT)
Issue Date: Nov-2017
Publisher: Springer Nature America, Inc
Journal title: Journal of High Energy Physics
Volume: 2017
Thesis number: 97
Abstract: We propose an optimization procedure for Euclidean path-integrals that evaluate CFT wave functionals in arbitrary dimensions. The optimization is performed by minimizing certain functional, which can be interpreted as a measure of computational complexity, with respect to background metrics for the path-integrals. In two dimensional CFTs, this functional is given by the Liouville action. We also formulate the optimization for higher dimensional CFTs and, in various examples, find that the optimized hyperbolic metrics coincide with the time slices of expected gravity duals. Moreover, if we optimize a reduced density matrix, the geometry becomes two copies of the entanglement wedge and reproduces the holographic entanglement entropy. Our approach resembles a continuous tensor network renormalization and provides a concrete realization of the proposed interpretation of AdS/CFT as tensor networks. The present paper is an extended version of our earlier report arXiv:1703.00456 and includes many new results such as evaluations of complexity functionals, energy stress tensor, higher dimensional extensions and time evolutions of thermofield double states.
Rights: © The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
DOI(Published Version): 10.1007/JHEP11(2017)097
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