From correlation functions to Wilson loops

TL;DR

This paper demonstrates how certain limits of correlation functions in conformal gauge theories can produce polygonal Wilson loops, with detailed analysis and perturbative checks in N=4 super-Yang-Mills.

Contribution

It establishes a precise connection between correlation functions and Wilson loops via a specific null limit, including detailed treatment of the propagation effects.

Findings

Correlation functions in conformal theories can generate Wilson loops in a specific limit.

Explicit perturbative checks confirm the theoretical predictions.

The approach clarifies the role of fast-moving particles in the limit.

Abstract

We start with an n-point correlation function in a conformal gauge theory. We show that a special limit produces a polygonal Wilson loop with $n$ sides. The limit takes the $n$ points towards the vertices of a null polygonal Wilson loop such that successive distances $x^2_{i,i+1} \to 0$. This produces a fast moving particle that generates a "frame" for the Wilson loop. We explain in detail how the limit is approached, including some subtle effects from the propagation of a fast moving particle in the full interacting theory. We perform perturbative checks by doing explicit computations in N=4 super-Yang-Mills.