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

Abstract

We derive the 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|. Its analytic continuation to negative |n| in the leading logarithmic approximation allows us to obtain residues of anomalous dimensions γof 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 γat 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.

45 pages, latex. In the last version the expression (16) for the t-channel partial wave of the process e+e- --> μ+μ- in the double-logarithmic approximation at QED is corrected and its derivation is given in the Appendix D

References in corpus (2)

• Anomalous dimensions of Wilson operators in N=4 SYM theory
• High-Energy QCD Asymptotics of Photon-Photon Collisions

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