After a brief review of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) approach to Regge processes in QCD and in supersymmetric gauge theories we propose a strategy for calculating the next-to-next-to-leading order corrections to the BFKL kernel. They can be obtained in terms of various cross sections for Reggeized gluon interactions. The corresponding amplitudes can be calculated in the framework of the effective action for high-energy scattering. In the case of $N=4$ supersymmetry it is also possible to use the Bern-Dixon-Smirnov ansatz. For this purpose the analytic properties of the Bern-Dixon-Smirnov amplitudes at high energies are investigated, in order to verify their self-consistency. It is found that, for the number of external particles being larger than 5, these amplitudes, beyond one loop, are not in agreement with the BFKL approach which predicts the existence of Regge cuts in some physical channels.

• Received 28 March 2008

DOI:https://doi.org/10.1103/PhysRevD.80.045002