Holography, Duality and Higher-Spin Theories

TL;DR

This work surveys the holographic relation between higher-spin theories on $AdS_4$ and conformal field theories, with emphasis on the holographic dual of the 3D $O(N)$ vector model. It identifies boundary double-trace deformations as a doorway to duality transformations, and shows that a bulk canonical transformation in $AdS_4$ implements an $S$-duality–like action on boundary correlators, forming an $SL(2,\mathbb{Z})$ structure that extends to linearized HS theories. The analysis connects the boundary generating functional to a bulk higher-spin action with couplings that scale with $N$, clarifying how boundary CFT data encode bulk HS physics and suggesting deep links to string dualities in the tensionless limit. Overall, it highlights a modular, duality-rich picture for HS holography, with potential implications for UV completions, observable 3D phenomena, and the pursuit of a complete bulk HS action.

Abstract

I review recent work on the holographic relation between higher-spin theories in Anti-de Sitter spaces and conformal field theories. I present the main results of studies concerning the higher-spin holographic dual of the three-dimensional O(N) vector model. I discuss the special role played by certain double-trace deformations in Conformal Field Theories that have higher-spin holographic duals. Using the canonical formulation I show that duality transformations in a U(1) gauge theory on AdS4 induce boundary double-trace deformations. I argue that a similar effect takes place in the holography of linearized higher-spin theories on AdS4.

Figures (2)

• Figure 1: Type 1 holographic correspondence: ${\cal N}=4$ SYM/IIB string theory.
• Figure 2: Type 2 holographic correspondence: O(N) vector model/HS on AdS$_4$.