Institut fur Theoretische Teilchenphysik, Universitat Karsruhe,
D-76128 Karsruhe,  GERMANY;
Bogoliubov Lab. of Theoretical Physics,
Joint Institute for Nuclear Research,
141980 Dubna, Moscow Region, RUSSIA

Equations of evolution in supersymmetric gauge theories

The Dokshitzer-Gribov-Lipatov-Altareli-Parisi (DGLAP) and Balitsky-Fadin-Kuraev-Lipatov (BFKL) evolution equations in the N = 4 supersymmetric gauge theory in the next-to-leading approximation are derived. The eigenvalue of the BFKL kernel in this model turns out to be an analytic function of the conformal spin |n|. Its analytic continuation to negative |n| in the leading logarithmic approximation allows to obtain residues of anomalous dimensions g of twist-2 operators in the non-physical points j = 0, -1, ... from the BFKL equation in an agreement with their direct calculation from the DGLAP equation. Moreover, in the multi-color limit of the N = 4 model the BFKL and DGLAP dynamics in the leading logarithmic approximation is integrable for an arbitrary number of particles. In the next-to-leading approximation the holomorphic separability of the Pomeron hamiltonian is violated, but the corresponding Bethe-Salpeter kernel has the property of a hermitian separability. The main singularities of anomalous dimensions g at j = -r obtained from the BFKL and DGLAP equations in the next-to-leading approximation coincide but our accuracy is not enough to verify an agreement for residues of subleading poles.