AdS Dual of the Critical O(N) Vector Model

TL;DR

This paper proposes a duality between a large N conformal field theory in 3 dimensions, specifically the critical O(N) vector model, and a higher-spin gauge theory in 4-dimensional anti-de Sitter space, establishing a new holographic correspondence.

Contribution

It introduces a conjectured duality linking the critical 3D O(N) model to a minimal bosonic higher-spin theory in AdS4, expanding the scope of holographic dualities.

Findings

The singlet sector of the critical O(N) model corresponds to a higher-spin gauge theory in AdS4.

The duality is established in the large N limit, connecting conformal field theories and higher-spin gravity.

Provides a framework for understanding holography beyond string theory with higher-spin 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 $(\phi^a \phi^a)^2$ interaction is dual, in the large $N$ limit, to the minimal bosonic theory in $AdS_4$ containing massless gauge fields of even spin.