Light-like Wilson loop correlators

TL;DR

This paper explores correlation functions of multiple light-like Wilson loops in \\mathcal{N}=4 super Yang-Mills theory, extending known dualities and equations to more complex loop configurations and sectors.

Contribution

It introduces the study of correlation functions of multiple light-like Wilson loops and verifies their properties in Abelian theory, extending the \\bar{Q}-equation to these cases.

Findings

Correlation functions obey a generalized \\bar{Q}-equation in Abelian theory.

Explicit calculations confirm the natural extension of known dualities.

Results set the stage for further non-Abelian and non-perturbative studies.

Abstract

It is well-known that the expectation values of null polygonal Wilson loops computed in planar \(\mathcal{N}=4\) super Yang-Mills theory are dual to MHV amplitudes in that theory, and moreover that the duality can be extended to higher helicity sectors through the introduction of super Wilson loops. In this first of a series of papers, we investigate the natural generalisation posed by correlation functions of multiple light-like loop operators, both in the bosonic case and in the case of super Wilson loops. Explicit calculations are presented in several cases and we verify that, in the Abelian theory, these objects obey a natural generalisation of the \(\bar{Q}\)-equation which relates different loop orders, kinematic configurations and Grassmann sectors.