Towards deriving the AdS/CFT correspondence

I present the sketch of a "physicist's" derivation of the AdS/CFT correspondence for the original pair, string theory in $AdS_5\times S^5$ vs. ${\cal N}=4$ SYM, based on the pp wave limit, and deviations from it. I show that one can reverse the logic, and derive the action of ${\cal N}=4$ SYM, as kinetic terms plus vertices, as well as the elements of its path integral, from string theory on the pp wave. One can also treat consistently deviations from the "strings on the pp wave" limit, starting from the SYM side, and a priori reconstruct the full $AdS_5\times S^5$ geometry perturbatively, as well as full perturbative string theory on it.