AdS Dual of the Critical O(N) Vector Model

TL;DR

The paper proposes a concrete AdS/CFT-like duality between large-N vector models and higher-spin gauge theories in AdS, focusing on the 3D critical O(N) vector model and the minimal bosonic higher-spin theory in AdS_4 with only even spins. It argues that the singlet sector maps to an infinite tower of massless higher-spin fields in AdS_4, with boundary currents J_{(μ1...μs)} corresponding to bulk fields, and explores the role of operator dimensions, Δ_± branches, and the IR fixed point where Δ_J=2. Through analysis of OPEs and 4-point functions at large N, the work shows that higher-spin exchanges are essential to reproduce the CFT data, providing a tractable example of higher-spin holography and suggesting broad extensions to non-minimal algebras and other dimensions. The results illuminate how vector-model holography can serve as a simpler arena for understanding AdS/CFT with an infinite set of bulk gauge fields.

Abstract

We suggest a general relation between theories of infinite number of higher-spin massless gauge fields in $AdS_{d+1}$ and large $N$ conformal theories in $d$ dimensions containing $N$-component vector fields. In particular, we propose that the singlet sector of the well-known critical 3-d O(N) model with the $(φ^a φ^a)^2$ interaction is dual, in the large $N$ limit, to the minimal bosonic theory in $AdS_4$ containing massless gauge fields of even spin.