Canonical Formulation of $O(N)$ Vector/Higher Spin Correspondence

Abstract

We discuss the canonical structure of the collective formulation of Vector Model/Higher Spin Duality in AdS${}_4$. This involves a construction of bulk AdS Higher Spin fields through a time-like bi-local Map, with a Hamiltonian and canonical structure which are established to all orders in $1/N$.

24 pages; v2: minor changes, references added, version to be submitted to J. Phys. A; v3: reference added and typos corrected. Minor improved. An appendix about algebra of bi-local operators added

References in corpus (6)

• AdS_4/CFT_3 Construction from Collective Fields
• Holographic dual of free field theory
• The Holographic Geometry of the Renormalization Group and Higher Spin Symmetries
• The Exact Renormalization Group and Higher-spin Holography
• 1/N and Loop Corrections in Higher Spin AdS_4/CFT_3 Duality
• Finite N and the failure of bulk locality: Black holes in AdS/CFT

Cited by in corpus (21)

• Light-Front Holographic QCD and Emerging Confinement
• Summing over Geometries in String Theory
• Space-Time in the SYK Model
• SYK Models and SYK-like Tensor Models with Global Symmetry
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• AdS Maps and Diagrams of Bi-local Holography
• A Derivation of AdS/CFT for Vector Models
• Holographic Representation of Higher Spin Gauge Fields
• Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality
• Holography of Information in AdS/CFT
• Higher-spin symmetry vs. boundary locality, and a rehabilitation of dS/CFT
• Four point functions in CFT's with slightly broken higher spin symmetry
• Chaos in Three-dimensional Higher Spin Gravity
• Large N bilocals at the infrared fixed point of the three dimensional O(N) invariant vector theory with a quartic interaction
• On (spinor)-helicity and bosonization in $Ad{S}_4/CF{T}_3$
• Quantum Error Correction and Holographic Information from Bilocal Holography
• Explicit holography for vector models at finite $N$, volume and temperature
• Holography for Tensor models
• Holographic quantization of linearized higher-spin gravity in the de Sitter causal patch
• AdS from CFT for scalar QED
• Cutoff Function in Holographic RG Flow