Pulling the straps of polygons

TL;DR

This paper derives a simple formula for the discontinuities of two-loop Wilson loop results using the Operator Product Expansion, and argues these discontinuities can determine the full two-loop answer for polygons, exemplified by the hexagon.

Contribution

It introduces a method to compute two-loop Wilson loop discontinuities from one-loop results, simplifying higher-loop calculations for polygons.

Findings

Derived a formula for two-loop Wilson loop discontinuities

Showed discontinuities can determine the full two-loop result

Explicitly applied to the hexagon case

Abstract

Using the Operator Product Expansion for Wilson loops we derive a simple formula giving the discontinuities of the two loop result in terms of the one loop answer. We also argue that the knowledge of these discontinuities should be enough to fix the full two loop answer, for a general number of sides. We work this out explicitly for the case of the hexagon and rederive the known result.