Classical Polylogarithms for Amplitudes and Wilson Loops

Abstract

We present a compact analytic formula for the two-loop six-particle maximally helicity violating remainder function (equivalently, the two-loop lightlike hexagon Wilson loop) in $\mathcal{N}=4$ supersymmetric Yang-Mills theory in terms of the classical polylogarithm functions ${\mathrm{Li}}_{k}$ with cross ratios of momentum twistor invariants as their arguments. In deriving our formula we rely on results from the theory of motives.