On the two-loop hexagon Wilson loop remainder function in [formula omitted] SYM

Jian-Hui Zhang

doi:10.1016/j.physletb.2011.01.056

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.

Highlights

In the past few years much progress has been made in understanding scattering amplitudes in gauge theories, and in particular in N = 4 supersymmetric Yang-Mills (SYM) theory
Given the well-known structure of the IR divergences of gluon amplitudes [3], the BDS ansatz proposes an explicit expression for the finite part of the planar gluon MHV amplitude with an arbitrary number of external gluons, to all orders in ’t Hooft coupling
In this paper we present an alternate, more compact representation for the two-loop hexagon Wilson loop remainder function, based on the observation that the conformal-crossratio-dependent terms in the BDS ansatz exhibit a simple structure when written in an integral form, and on the result of [19] as well as on the general properties of multiple polylogarithms described in refs. [24, 25]

Summary

Introduction

Explicit numerical computations for the two-loop hexagon Wilson loop [13, 15] showed that the complete result differs from the BDS ansatz by a finite remainder function, which depends only on the conformal cross ratios. In this paper we present an alternate, more compact representation for the two-loop hexagon Wilson loop remainder function, based on the observation that the conformal-crossratio-dependent terms in the BDS ansatz exhibit a simple structure when written in an integral form, and on the result of [19] as well as on the general properties of multiple polylogarithms described in refs. Note that R6WL,(2) is a function of u1, u2, u3 only

The two-loop hexagon Wilson loop remainder function

Conclusions