Holography, Unfolding and Higher-Spin Theory

TL;DR

This paper explores holographic duality through unfolded formulations, illustrating how higher-spin theories in AdS spaces relate to boundary conformal theories, including nonlinear and free cases, and extends to nonrelativistic quantum mechanics.

Contribution

It demonstrates the equivalence of different higher-spin models via unfolded formulations and explores their holographic duals across various dimensions and contexts.

Findings

Higher-spin gauge theories in AdS_4 are dual to 3d conformal currents with interactions.

Identified reductions where boundary theories are free, matching known duals.

Extended holographic duality to AdS_3/CFT_2 and nonrelativistic quantum mechanics.

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 $AdS_4$ 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 $AdS_4$ 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 $AdS_3/CFT_2$ 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.