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

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

2002-08-23

arxiv.org/abs/hep-ph/0208220v3

Nucl.Phys.B661:19-61,2003; Erratum-ibid.B685:405-407,2004

Physics

High Energy Physics

High Energy Physics - Phenomenology

45 pages, latex. In the last version the expression (16) for the t-channel partial wave of the process e+e- --> \mu+\mu- in th

Scientific paper

10.1016/S0550-3213(03)00264-5

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 \gamma 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 \gamma 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.

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