Cusped light-like Wilson loops in gauge theories

TL;DR

This paper introduces a new method for analyzing light-like Wilson loops with cusps in gauge theories, connecting their geometric properties with their renormalization behavior.

Contribution

It generalizes the quantum dynamical principle to handle singularities in cusped light-like Wilson loops, establishing a differential equation linking area variations and renormalization.

Findings

Wilson loops obey a differential equation relating area and renormalization

Method handles singularities from light-like cusps effectively

Potential link between loop geometry and area evolution

Abstract

We propose and discuss a new approach to the analysis of the correlation functions which contain light-like Wilson lines or loops, the latter being cusped in addition. The objects of interest are therefore the light-like Wilson null-polygons, the soft factors of the parton distribution and fragmentation functions, high-energy scattering amplitudes in the eikonal approximation, gravitational Wilson lines, etc. Our method is based on a generalization of the universal quantum dynamical principle by J. Schwinger and allows one to take care of extra singularities emerging due to light-like or semi-light-like cusps. We show that such Wilson loops obey a differential equation which connects the area variations and renormalization group behavior of those objects and discuss the possible relation between geometrical structure of the loop space and area evolution of the light-like cusped Wilson loops.