Canonical Formulation of $O(N)$ Vector/Higher Spin Correspondence

We discuss the canonical structure of the collective formulation of Vector Model/Higher Spin Duality in AdS$_4$. This involves a construction of bulk AdS Higher Spin fields through a time-like bi-local Map, with a Hamiltonian and canonical structure which are established to all orders in $1/N$.
Comment: 24 pages; v2: minor changes, references added, version to be submitted to J. Phys. A; v3: reference added and typos corrected. Minor improved. An appendix about algebra of bi-local operators added