DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory

We discuss DGLAP and BFKL evolution equations in the N = 4 supersymmetric gauge theory in the leading and next-to-leading approximations. Eigenvalues of the BFKL kernel in this model turn out to be analytic functions of the conformal spin. It allows us to find the residues of the anomalous dimensions of the twist-2 operators in the points j = 1, 0,−1, .... from the BFKL equation in an agreement with their direct calculation from the DGLAP equation. The holomorphic separability of the BFKL kernel and the integrability of the DGLAP dynamics in this model are also discussed. PACS: 12.38.Bx