An Operator Product Expansion for Polygonal null Wilson Loops

TL;DR

This paper develops an operator product expansion for null polygonal Wilson loops in conformal gauge theories, including subleading corrections, and verifies it at strong and weak coupling, providing new insights into their structure.

Contribution

It introduces a systematic OPE-like expansion for polygonal Wilson loops with null edges, including subleading corrections governed by high spin excitations, applicable across all conformal gauge theories.

Findings

Validated the expansion at strong coupling for N=4 super Yang Mills.

Confirmed the expansion at two loops in weak coupling.

Predicted higher-loop behavior of the remainder function.

Abstract

We consider polygonal Wilson loops with null edges in conformal gauge theories. We derive an OPE-like expansion when several successive lines of the polygon are becoming aligned. The limit corresponds to a collinear, or multicollinear, limit and we explain the systematics of all the subleading corrections, going beyond the leading terms that were previously considered. These subleading corrections are governed by excitations of high spin operators, or excitations of a flux tube that goes between two Wilson lines. The discussion is valid for any conformal gauge theory, for any coupling and in any dimension. For N=4 super Yang Mills we check this expansion at strong coupling and at two loops at weak coupling . We also make predictions for the remainder function at higher loops. In the process, we also derived a new version for the TBA integral equations that determine the strong coupling answer and present the area as the associated Yang-Yang functional.