BFKL approach and 2→5 maximally helicity violating amplitude in N=4 super-Yang-Mills theory

We study maximally helicity violating amplitude for the 2→5 scattering in the multi-Regge kinematics. The Mandelstam cut correction to the Bern-Dixon-Smirnov amplitude is calculated in the leading logarithmic approximation and the corresponding remainder function is given to any loop order in a closed integral form. We show that the leading logarithmic approximation remainder function at two loops for 2→5 amplitude can be written as a sum of two 2→4 remainder functions due to recursive properties of the leading order impact factors. We also make some generalizations for the maximally helicity violating amplitudes with more external particles. The results of the present study are in agreement with the all leg two-loop symbol derived by Caron-Huot as shown in a parallel paper of one of the authors with collaborators.