An Elliptic Generalization of Multiple Polylogarithms

TL;DR

This paper introduces a new class of elliptic functions generalizing multiple polylogarithms, useful in quantum field theory calculations, and explores their properties and relations.

Contribution

It presents the first elliptic generalization of multiple polylogarithms, including their properties, weight reduction, and foundational relations.

Findings

Functions appear in two-loop massive sunrise graph calculations

Weight can be lowered via differential operators

Properties and relations can be studied from lower weights

Abstract

We introduce a class of functions which constitutes an obvious elliptic generalization of multiple polylogarithms. A subset of these functions appears naturally in the \epsilon-expansion of the imaginary part of the two-loop massive sunrise graph. Building upon the well known properties of multiple polylogarithms, we associate a concept of weight to these functions and show that this weight can be lowered by the action of a suitable differential operator. We then show how properties and relations among these functions can be studied bottom-up starting from lower weights.