Classical Polylogarithms for Amplitudes and Wilson Loops

TL;DR

This paper provides a compact analytic formula for a two-loop six-particle amplitude in N=4 SYM theory using classical polylogarithms, connecting advanced mathematical concepts with quantum field theory calculations.

Contribution

It introduces a novel compact expression for the two-loop six-particle MHV remainder function utilizing classical polylogarithms and motives, advancing the analytic understanding of scattering amplitudes.

Findings

Explicit formula for the two-loop six-particle MHV remainder function

Connection between polylogarithms and motives in amplitude calculations

Simplification of complex amplitude expressions

Abstract

We present a compact analytic formula for the two-loop six-particle MHV remainder function (equivalently, the two-loop light-like hexagon Wilson loop) in N = 4 supersymmetric Yang-Mills theory in terms of the classical polylogarithm functions Li_k with cross-ratios of momentum twistor invariants as their arguments. In deriving our result we rely on results from the theory of motives.