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

TL;DR

The paper analyzes the duality between planar N=4 SYM gluon MHV amplitudes and light-like Wilson loops, focusing on the six-point two-loop case where a finite remainder beyond the BDS ansatz arises. It reviews the duality framework and remainder function definition, and introduces a new, compact integral representation for the two-loop hexagon Wilson loop remainder that depends on conformal cross ratios and matches previous results. The authors demonstrate the approach in both equal and general cross-ratio configurations, highlighting improved analytic structure and potential utility for constraining the BDS ansatz and relating weak and strong coupling results. This work enhances understanding of the remainder function’s form and its role in the amplitude-Wilson loop correspondence across couplings.

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.