Holography, Duality and Higher-Spin Theories

TL;DR

This paper reviews the holographic duality between higher-spin theories in Anti-de Sitter spaces and conformal field theories, focusing on the three-dimensional O(N) vector model and the role of double-trace deformations.

Contribution

It elucidates the connection between higher-spin holography and boundary deformations, highlighting the impact of duality transformations in gauge theories on AdS boundary conditions.

Findings

Higher-spin holography relates AdS higher-spin theories to CFTs.

Double-trace deformations are crucial in the holographic correspondence.

Duality transformations induce boundary deformations in the holographic setup.

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.