  We consider correlators of N=4 super Yang Mills of the form A ~ < O_1 O_2
O*_1 O*_2 >, where the operators O_1 and O_2 are scalar primaries. In
particular, we analyze this correlator in the planar limit and in a Lorentzian
regime corresponding to high energy interactions in AdS. The planar amplitude
is dominated by a Regge pole whose nature varies as a function of the 't Hooft
coupling g^2. At large g, the pole corresponds to graviton exchange in AdS,
whereas at weak g, the pole is that of the hard perturbative BFKL pomeron. We
concentrate on the weak coupling regime and analyze pomeron exchange directly
in position space. The analysis relies heavily on the conformal symmetry of the
transverse space E^2 and of its holographic dual hyperbolic space H_3,
describing with an unified language, both the weak and strong 't Hooft coupling
regimes. In particular, the form of the impact factors is highly constrained in
position space by conformal invariance. Finally, the analysis suggests a
possible AdS eikonal resummation of multi-pomeron exchanges implementing AdS
unitarity, which differs from the usual 4-dimensional eikonal exponentiation.
Relations to violations of 4-dimensional unitarity at high energy and to the
onset of nonlinear effects and gluon saturation become immediate questions for
future research.

High Energy Physics - Theory;High Energy Physics - Phenomenology