Analytic Results for MHV Wilson Loops

TL;DR

This paper derives concise analytic formulas for MHV Wilson loops on polygonal contours in N=4 SYM, valid for any number of edges, and relates them to scattering amplitudes in the AdS/CFT correspondence.

Contribution

It provides the first general analytic expressions for n-point polygonal Wilson loops at two loops in weakly coupled N=4 SYM, extending previous specific cases.

Findings

Analytic formulas valid for any number of edges.

Results applicable to polygons embedded in (1+1)-dimensional subspace.

Supports the conjecture relating Wilson loops to MHV scattering amplitudes.

Abstract

We obtain concise analytic formulae for Wilson loops computed on special n-point polygonal contours through two-loops in weakly coupled N=4 supersymmetric gauge theory. The contours we consider can be embedded into a (1+1)-dimensional subspace of the 4-dimensional gauge theory, corresponding to the boundary of the AdS_3 on the string theory side. Our analytic results hold for any number of edges, thus generalising to arbitrary n the recently derived expressions for 2-dimensional octagons. These polygonal Wilson loops have been conjectured to be equivalent to MHV scattering amplitudes in planar N=4 SYM.