DGLAP and BFKL Equations in Supersymmetric Gauge Theories

Abstract

We derive DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory in the next-to-leading approximation. The eigenvalue of the BFKL kernel in this model turns out to be an analytic function of the conformal spin |n|. The corresponding kernel for the Bethe-Salpeter equation has the property of the hermitian separability. The anomalous dimension matrix can be transformed to a triangle form with the use of the similarity transformation for the diagonalization of the anomalous dimension matrix in the leading order. The eigenvalues of these matrices can be expressed in terms of a universal function by an integer shift of its argument. We also investigate in this approximation possible relations between the DGLAP and BFKL equations.