Holography, Duality and Higher-Spin Theories

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.