Wilson loop remainder function for null polygons in the limit of self-crossing

TL;DR

This paper investigates the divergence behavior of Wilson loop remainder functions for null polygons with self-crossings, revealing a quadratic divergence at two loops influenced by conformal geometry factors.

Contribution

It introduces a novel RG-based approach to analyze divergences in self-crossing null polygons and derives explicit formulas for the two-loop remainder divergence.

Findings

Quadratic divergence in the two-loop remainder function.

Divergence depends on conformal cross-ratios.

RG techniques effectively analyze self-crossing configurations.

Abstract

The remainder function of Wilson loops for null polygons becomes divergent if two vertices approach each other. We apply RG techniques to the limiting configuration of a contour with self-intersection. As a result for the two loop remainder we find a quadratic divergence in the logarithm of the distance between the two approaching vertices. The divergence is multiplied by a factor, which is given by a pure number plus the product of two logarithms of cross-ratios characterising the conformal geometry of the self-crossing.