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We present in detail the basic ingredients contained in bi-local holography,representing a constructive scheme for reconstructing AdS bulk theories inVectorial/AdS duality. Explicit Mapping to bulk AdS and higher spin fields isseen to be given by a double Fourier transform. All order interactions areexplicitly specified through the collective action. This generates bulk Feynman(Witten) diagrams (at tree and loop level). We give details of the four-pointcase evaluation. It is noted that the bi-local construction goes beyond theassumptions in various discussions of non-locality.

AdS Maps and Diagrams of Bi-local Holography