Journal of High Energy Physics

, 2012:193 | Cite as

Holographic geometry of entanglement renormalization in quantum field theories

  • Masahiro Nozaki
  • Shinsei Ryu
  • Tadashi Takayanagi


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.


AdS-CFT Correspondence Holography and condensed matter physics (AdS/CMT) Renormalization Group 


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Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Masahiro Nozaki
    • 1
  • Shinsei Ryu
    • 2
  • Tadashi Takayanagi
    • 1
    • 3
  1. 1.Yukawa Institute for Theoretical PhysicsKyoto UniversityKyotoJapan
  2. 2.Department of PhysicsUniversity of Illinois at Urbana-ChampaignUrbanaU.S.A.
  3. 3.Kavli Institute for the Physics and Mathematics of the UniverseUniversity of TokyoKashiwaJapan

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