Unitary Networks from the Exact Renormalization of Wave Functionals

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 $Ad{S}_{d+1}$. 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.

31 pages (including appendices), 5 figures

References in corpus (8)

• Complexity and Shock Wave Geometries
• A Stereoscopic Look into the Bulk
• Bit threads and holographic entanglement
• Entanglement renormalization, scale invariance, and quantum criticality
• Consistency Conditions for an AdS/MERA Correspondence
• The Exact Renormalization Group and Higher-spin Holography
• Stringy effects in scrambling
• Higher Spin Fronsdal Equations from the Exact Renormalization Group

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• Wilsonian Renormalization as a Quantum Channel and the Separability of Fixed Points
• Exact renormalization group for wave functionals
• The Large $N$ Limit of icMERA and Holography
• Exact Renormalization of Wave Functionals yields Continuous MERA
• Towards holography for quantum mechanics
• A Lindbladian for exact renormalization of density operators in QFT