After defining the Regge limit of the CFT four point function, we shall study the Regge theory that controls the high energy behavior of four point function. In AdS/CFT we can test the Regge theory predictions both at weak and strong coupling. At weak coupling, the leading Regge pole is the well known hard pomeron of perturbative gauge theories. At strong coupling, the leading Regge pole comes from the graviton's Regge trajectory in string theory
Using this limit we can extract the scattering amplitudes of the bulk theory in flat space from the correlation functions of the dual CFT. This gives a non-perturbative definition of flat space string theory scattering amplitudes as a limit of the correlation functions of SYM.
The validity of a local AdS supergravity description of SYM at strong coupling requires the existence of a parametrically large gap in the spectrum of dimensions of the local operators, separating the low dimension operators dual to supergravity fields from the others. We shall give evidence that the reverse is also true: a large gap in the spectrum of dimensions implies a local bulk dual.
