Holography, Unfolding and Higher-Spin Theory

Abstract

Holographic duality is argued to relate classes of models that have equivalent unfolded formulation, hence exhibiting different space-time visualizations for the same theory. This general phenomenon is illustrated by the $Ad{S}_4$ higher-spin gauge theory shown to be dual to the theory of 3d conformal currents of all spins interacting with 3d conformal higher-spin fields of Chern-Simons type. Generally, the resulting 3d boundary conformal theory is nonlinear, providing an interacting version of the 3d boundary sigma model conjectured by Klebanov and Polyakov to be dual to the $Ad{S}_4$ HS theory in the large $N$ limit. Being a gauge theory it escapes the conditions of the theorem of Maldacena and Zhiboedov, which force a 3d boundary conformal theory to be free. Two reductions of particular higher-spin gauge theories where boundary higher-spin gauge fields decouple from the currents and which have free boundary duals are identified. Higher-spin holographic duality is also discussed for the cases of $Ad{S}_3/CF{T}_2$ and duality between higher-spin theories and nonrelativistic quantum mechanics. In the latter case it is shown in particular that ($dS$) $AdS$ geometry in the higher-spin setup is dual to the (inverted) harmonic potential in the quantum-mechanical setup.

57 pages, V2: Acknowledgements, references, comments, clarifications and new section on reductions of particular HS theories associated with free boundary theories are added. Typos corrected, V3. Minor corrections: clarification in section 9 is added and typos corrected

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• Canonical Formulation of $O(N)$ Vector/Higher Spin Correspondence
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• On holomorphic sector of higher-spin theory
• Test of the local form of higher-spin equations via AdS/CFT
• 4D Higher Spin Black Holes with Nonlinear Scalar Fluctuations
• Projectively-Compact Spinor Vertices and Space-Time Spin-Locality in Higher-Spin Theory
• BRST invariant effective action of shadow fields, conformal fields, and AdS/CFT
• Non-Relativistic Holography -- A Group-Theoretical Perspective
• Boundary values of mixed-symmetry massless fields in AdS space
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• Higher Spins in Hyper-Superspace
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