Holographic geometry of entanglement renormalization in quantum field theories

Masahiro Nozaki, Shinsei Ryu, Tadashi Takayanagi

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number193
JournalJournal of High Energy Physics
Issue number10
StatePublished - 2012
Externally publishedYes


  • ADS-CFT correspondence
  • Holography and condensed matter physics (AdS/CMT)
  • Renormalization group

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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