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

TL;DR

This paper computes the eigenvalues of the next-to-leading BFKL kernel in N=4 supersymmetric Yang-Mills theory, advancing understanding of high-energy scattering amplitudes and their collinear limits.

Contribution

It provides the eigenvalues of the NLO BFKL kernel in the adjoint representation for N=4 SUSY and applies them to analyze the six-point amplitude's high-energy behavior.

Findings

Eigenvalues of the NLO BFKL kernel obtained.

High-energy behavior of the six-point amplitude characterized.

Full agreement with the three-loop remainder function ansatz achieved.

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.