Light-like Wilson loops and the $\bar{Q}$-equation

TL;DR

This paper computes $O(g^2)$ correlators of multiple light-like Wilson loops in $SU(N)$ super Yang-Mills theory, verifying a generalized $ar{Q}$-equation that aids higher-order calculations.

Contribution

It extends the study of Wilson loop correlators to $SU(N)$ theory at one-loop order and confirms a generalized $ar{Q}$-equation for multiple loops.

Findings

Calculated $O(g^2)$ correlators of multiple light-like Wilson loops.

Verified the validity of the generalized $ar{Q}$-equation in $SU(N)$ theory.

Provided integrated expressions for loop correlators using chiral box expansion.

Abstract

In recent work we began a study of the correlators of multiple light-like Wilson loops in $\mathcal{N}=4$ super Yang-Mills theory, focussing primarily on tree-level calculations and, beyond tree-level, to the Abelian theory. Here we calculate $O(g^2)$ correlators of multiple light-like Wilson loops in the $SU(N)$ theory. We use the chiral box expansion and a study of the leading singularities of the loop integrand to arrive at integrated expressions for these objects. We then use the results of these calculations to verify that a natural generalisation of the $\bar{Q}$-equation, familiar from the study of single Wilson loops, holds in the $SU(N)$ theory. This $\bar{Q}$-equation should provide a valuable tool for the computation of multiple Wilson loop correlators at higher order in the coupling.