  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.

High Energy Physics - Theory