Perturbative and Non-Perturbative Aspects in Vector Model/Higher Spin Duality

Abstract

We review some recent work on AdS/CFT duality involving the 3d O(N) Vector Model and AdS4 Higher Spin Gravity. Our construction is based on bi-local collective field theory which provides an off-shell formulation of Higher Spin Gravity with G = 1/N playing the role of a coupling constant. Consequently perturbative and non-perturbative issues of the theory can be studied. For the correspondence based on free CFT's we discuss the nature of bulk 1/N interactions through an S-matrix which is argued to be equal to 1 (Coleman-Mandula theorem). As a consequence in this class of theories nonlinearities are removable, through a nonlinear field transformation which we show at the exact level. We also describe a geometric (Kahler space) framework for the bi-local theory which applies equally simple to Sp(2N) fermions and the de Sitter correspondence. We discuss in this framework the structure and size of the bi-local Hilbert space and the implementation of (finite N) exclusion principle.

21 pages, 3 figures; Contribution to J. Phys. A special volume on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasiliev; v2: references updated

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• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• AdS_4/CFT_3 Construction from Collective Fields
• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• Holographic dual of free field theory
• Higher Spins and Open Strings: Quartic Interactions
• Singleton deformation of higher-spin theory and the phase structure of the three-dimensional O(N) vector model

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• Multiparticle extension of the higher-spin algebra
• The $\mathcal{N}=1$ algebra ${\mathcal{W}}_{\infty }[\mu ]$ and its truncations
• Massive Higher Spin Fields Coupled to a Scalar: Aspects of Interaction and Causality
• Light-cone gauge approach to arbitrary spin fields, currents, and shadows
• Light-cone AdS/CFT-adapted approach to AdS fields/currents, shadows, and conformal fields
• Evidence for Gauge/Gravity Correspondence for D$p$-branes at Weak 't Hooft Coupling
• Higher Spins at the Quintic Order: Localization Effect and Simplifications
• Higher Spin Gravity and Exact Holography
• Symmetries and Invariants in Higher-Spin Theory