Six-point remainder function in multi-Regge-kinematics: an efficient approach in momentum space

TL;DR

This paper introduces a momentum space formalism for calculating the six-point remainder function in N=4 super-Yang-Mills theory, enabling efficient perturbative computations up to high loop orders in multi-Regge kinematics.

Contribution

It develops a recursive integral identity-based approach to compute the remainder function directly in momentum space, extending calculations up to 10 loops and confirming an all-loop leading logarithmic formula.

Findings

Accessed the full remainder function up to 7 loops in multi-Regge kinematics.

Extended calculations to 10 loops in the fourth logarithmic order.

Proved the all-loop formula for the leading logarithmic approximation.

Abstract

Starting from the known all-order expressions for the BFKL eigenvalue and impact factor, we establish a formalism allowing the direct calculation of the six-point remainder function in N=4 super-Yang-Mills theory in momentum space to - in principle - all orders in perturbation theory. Based upon identities which relate different integrals contributing to the inverse Fourier-Mellin transform recursively, the formalism allows to easily access the full remainder function in multi-Regge kinematics up to 7 loops and up to 10 loops in the fourth logarithmic order. Using the formalism, we prove the all-loop formula for the leading logarithmic approximation proposed by Pennington and investigate the behavior of several newly calculated functions.