Real valued functions for BFKL eigenvalue

TL;DR

This paper introduces new real-valued functions of complex variables to describe the BFKL eigenvalue in N=4 super Yang-Mills theory, proposing a comprehensive functional space for all perturbative orders.

Contribution

It defines a novel class of functions with a fixed complexity that generalizes the known eigenvalue expressions, potentially unifying their structure across perturbation orders.

Findings

New functions form a basis for BFKL eigenvalues at all orders.

Functions have a fixed complexity analogous to harmonic sum weights.

Proposes a unifying functional framework for BFKL eigenvalues.

Abstract

We consider known expressions for the eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation in $N=4$ super Yang-Mills theory as a real valued function of two variables anomalous dimension and the conformal spin. We define new real valued functions of two complex conjugate variables that have a definite complexity analogous to the weight of the nested harmonic sums. We argue that those functions span a general space of functions for the BFKL eigenvalue at any order of the perturbation theory.