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

TL;DR

This work investigates the interplay between DGLAP and BFKL evolution in N=4 supersymmetric gauge theory, focusing on leading and next-to-leading order corrections and revealing analytic, holomorphically separable structures in the BFKL kernel that enable cross-checks with DGLAP anomalous dimensions.By deriving explicit NLO BFKL eigenvalues and their holomorphic decomposition, the authors show that anomalous dimensions of twist-2 operators can be obtained through analytic continuation to negative conformal spins, reinforcing a deep link between Regge and Bjorken regimes in a conformal theory with vanishing beta function.The paper also presents LO anomalous-dimension matrices and proposes a universal NLO anomalous dimension for multiplicatively renormalizable twist-2 operators, supported by a DRED-friendly scheme and the anticipated integrability of the reggeon dynamics in the Maldacena (N=4) framework.Overall, the results suggest that in N=4 SUSY the DGLAP and BFKL evolutions are not independent, with integrability and holomorphic separability guiding the structure of higher-order corrections and potentially enabling exact or highly constrained descriptions of parton evolution in this theory.

Abstract

We discuss DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory in the leading and next-to-leading approximations. Eigenvalues of the BFKL kernel in this model turn out to be analytic functions of the conformal spin. It allows us to find the residues of the anomalous dimensions of the twist-2 operators in the points j=1,0,-1, ... from the BFKL equation in an agreement with their direct calculation from the DGLAP equation. The holomorphic separability of the BFKL kernel and the integrability of the DGLAP dynamics in this model are also discussed.