Towards single-valued polylogarithms in two variables for the seven-point remainder function in multi-Regge-kinematics

TL;DR

This paper develops two-variable single-valued polylogarithms and applies them to compute the seven-point remainder function in N=4 super-Yang-Mills theory within the multi-Regge regime, achieving five-loop accuracy.

Contribution

It introduces a new class of two-variable single-valued polylogarithms and uses them to calculate the seven-point remainder function at five loops.

Findings

Constructed two-dimensional single-valued polylogarithms.

Computed the leading logarithmic approximation up to five loops.

Enhanced understanding of multi-Regge kinematics in supersymmetric gauge theories.

Abstract

We investigate single-valued polylogarithms in two complex variables, which are relevant for the seven-point remainder function in N=4 super-Yang-Mills theory in the multi-Regge regime. After constructing these two-dimensional polylogarithms, we determine the leading logarithmic approximation of the seven-point remainder function up to and including five loops.