BFKL equation for the adjoint representation of the gauge group in the next-to-leading approximation at N=4 SUSY

Abstract

We calculate the eigenvalues of the next-to-leading kernel for the BFKL equation in the adjoint representation of the gauge group $SU(N_c)$ in the N=4 supersymmetric Yang-Mills model. These eigenvalues are used to obtain the high energy behavior of the remainder function for the 6-point scattering amplitude with the maximal helicity violation in the kinematical regions containing the Mandelstam cut contribution. The leading and next-to-leading singularities of the corresponding collinear anomalous dimension are calculated in all orders of perturbation theory. We compare our result with the known collinear limit and with the recently suggested ansatz for the remainder function in three loops and obtain the full agreement providing that the numerical parameters in this anzatz are chosen in an appropriate way.

13 pages

References in corpus (13)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• The Pomeron and Gauge/String Duality
• Bootstrapping the three-loop hexagon
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• Dressing and Wrapping
• NLO evolution of color dipoles in N=4 SYM
• Proof of the multi-Regge form of QCD amplitudes with gluon exchanges in the NLA
• Integrability of scattering amplitudes in N=4 SUSY
• BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills
• Unbound exotic nuclei studied by projectile fragmentation
• Mandelstam cuts and light-like Wilson loops in N=4 SUSY
• The dipole form of the gluon part of the BFKL kernel
• Collinear and Regge behavior of 2 -> 4 MHV amplitude in N = 4 super Yang-Mills theory

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