On the two-loop hexagon Wilson loop remainder function in N=4 SYM

TL;DR

This paper presents a more compact analytical expression for the two-loop hexagon Wilson loop remainder function in N=4 super Yang-Mills theory, improving understanding of duality with gluon amplitudes.

Contribution

It introduces an alternative, simplified representation of the two-loop hexagon Wilson loop remainder function, enhancing computational and conceptual clarity.

Findings

New compact analytical form for the remainder function

Simplifies dependence on conformal cross ratios

Facilitates comparisons with gluon amplitude results

Abstract

A duality relation has been proposed between the planar gluon MHV amplitudes and light-like Wilson loops in N=4 super Yang-Mills. At six-point two-loop, the results for the planar gluon MHV amplitude and for the light-like Wilson loop agree, but they both differ from the Bern-Dixon-Smirnov ansatz by a finite remainder function. Recently Del Duca, Duhr and Smirnov presented an analytical result for the two-loop hexagon Wilson loop remainder function in general kinematics. Their result is rather lengthy, and the dependence on the conformal cross ratios appears in a complicated way. Here we present an alternate, more compact representation for the two-loop hexagon Wilson loop remainder function.