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

Aug, 2002
42 pages
Published in:
  • Nucl.Phys.B 661 (2003) 19-61,
  • Nucl.Phys.B 685 (2004) 405-407 (erratum)
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Abstract: (Elsevier)
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 γ 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 γ 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.
Note:
  • 45 pages, latex. In the last version the expression (16) for the t-channel partial wave of the process e+e- --> \mu+\mu- in the double-logarithmic approximation at QED is corrected and its derivation is given in the Appendix D
  • 12.38.Bx
  • gauge field theory
  • supersymmetry: model
  • DGLAP equation
  • Lipatov equation
  • correction: higher-order
  • spin: conformal
  • analytic properties
  • effect: higher-twist
  • cross section: high energy behavior