Summary: 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 AdS\(_4\) 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 AdS\(_4\) higher spin 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 AdS\(_3\)/CFT\(_2\) 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.
This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Higher spin theories and holography’.