NLO corrections to the BFKL equation in QCD and in supersymmetric gauge theories

We study next-to-leading corrections to the integral kernel of the BFKL equation for high-energy cross-sections in QCD and in supersymmetric gauge theories. The eigenvalue of the BFKL kernel is calculated in an analytic form as a function of the anomalous dimension gamma of the local gauge-invariant operators and their conformal spin n. For the case of an extended N = 4 SUSY, the kernel is significantly simplified, In particular, the terms nonanalytic in n are canceled. We discuss the relation between the DGLAP acid BFKL equations in the N = 4 model. (C) 2000 Elsevier Science B.V. All rights reserved.