DGLAP and BFKL equations in the \(N=4\) supersymmetric gauge theory
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Publication:1566265
DOI10.1016/S0550-3213(03)00264-5zbMATH Open1040.81062arXivhep-ph/0208220OpenAlexW3102717599WikidataQ56968067 ScholiaQ56968067MaRDI QIDQ1566265
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Publication date: 1 June 2003
Published in: (Search for Journal in Brave)
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 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.
Full work available at URL: https://arxiv.org/abs/hep-ph/0208220
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