  We compute, in N=4 super Yang-Mills theory, the four point correlation
function of R-currents in the Regge limit in the leading logarithmic
approximation at weak coupling. Such a correlator is the closest analog to
photon-photon scattering within QCD, and there is a well-defined procedure to
perform the analogous computation at strong coupling via the AdS/CFT
correspondence. The main result of this paper is, on the gauge theory side, the
proof of Regge factorization and the explicit computation of the R-current
impact factors.
