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

TL;DR

This work derives the next-to-leading order BFKL kernel in the adjoint representation for N=4 SYM and computes its eigenvalues to access the high-energy behavior of the 6-point MHV remainder function in Mandelstam-cut regions. By constructing the Green function from these eigenvalues, the authors obtain corrections to the remainder function $R_6$ up to three loops, demonstrating agreement with the DDH ansatz and extracting structure for impact-factor corrections through $\rho(w,w^*)$. They also connect these results to the collinear limit, deriving the leading and next-to-leading singularities of the collinear anomalous dimension $\gamma_{col}(\omega)$ in the Mandelstam region, and show consistency with known collinear limits. The findings reinforce the integrable, conformal aspects of the BFKL approach in $N=4$ SUSY and provide a cross-check between Regge, collinear, and multi-loop perturbative structures relevant for high-energy scattering amplitudes.

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.