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Holographic geometry of entanglement renormalization in quantum field theories

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Abstract

We study a conjectured connection between AdS/CFT and a real-space quantum renormalization group scheme, the multi-scale entanglement renormalization ansatz (MERA). By making a close contact with the holographic formula of the entanglement entropy, we propose a general definition of the metric in the MERA in the extra holographic direction. The metric is formulated purely in terms of quantum field theoretical data. Using the continuum version of the MERA (cMERA), we calculate this emergent holographic metric explicitly for free scalar boson and free fermions theories, and check that the metric so computed has the properties expected from AdS/CFT. We also discuss the cMERA in a time-dependent background induced by quantum quench and estimate its corresponding metric.

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Authors and Affiliations

  1. Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto, 606-8502, Japan

    Masahiro Nozaki & Tadashi Takayanagi

  2. Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green St, Urbana, IL, 61801, U.S.A.

    Shinsei Ryu

  3. Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa, Chiba, 277-8582, Japan

    Tadashi Takayanagi

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  1. Masahiro Nozaki
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  2. Shinsei Ryu
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  3. Tadashi Takayanagi
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Correspondence to Masahiro Nozaki.

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ArXiv ePrint: 1208.3469

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Nozaki, M., Ryu, S. & Takayanagi, T. Holographic geometry of entanglement renormalization in quantum field theories. J. High Energ. Phys. 2012, 193 (2012). https://doi.org/10.1007/JHEP10(2012)193

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