Unitary networks from the exact renormalization of wave functionals

Jackson R. Fliss, Robert G. Leigh, and Onkar Parrikar
Phys. Rev. D 95, 126001 – Published 6 June 2017

Abstract

The exact renormalization group (ERG) for O(N) vector models (at large N) on flat Euclidean space can be interpreted as the bulk dynamics corresponding to a holographically dual higher spin gauge theory on AdSd+1. This was established in the sense that at large N the generating functional of correlation functions of single-trace operators is reproduced by the on-shell action of the bulk higher spin theory, which is most simply presented in a first-order (phase space) formalism. In this paper, we extend the ERG formalism to the wave functionals of arbitrary states of the O(N) vector model at the free fixed point. We find that the ERG flow of the ground state and a specific class of excited states is implemented by the action of unitary operators which can be chosen to be local. Consequently, the ERG equations provide a continuum notion of a tensor network. We compare this tensor network with the entanglement renormalization networks, MERA, and its continuum version, cMERA, which have appeared recently in holographic contexts. In particular, the ERG tensor network appears to share the general structure of cMERA but differs in important ways. We comment on possible holographic implications.

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  • Received 15 March 2017

DOI:https://doi.org/10.1103/PhysRevD.95.126001

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

Jackson R. Fliss1, Robert G. Leigh1, and Onkar Parrikar1,2

  • 1Department of Physics, University of Illinois, 1110 West Green Street, Urbana, Illinois 61801, USA
  • 2David Rittenhouse Laboratory, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104, USA

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Issue

Vol. 95, Iss. 12 — 15 June 2017

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