High Energy Behavior of Wilson Lines

TL;DR

This paper studies the high energy behavior of open Wilson line correlators in noncommutative gauge theory, showing they tend to form closed loops, with proofs in weak coupling and implications for string theory calculations.

Contribution

It introduces a simple physical picture that open Wilson lines form closed loops at high energy and proves this in the weak coupling regime through perturbative analysis.

Findings

Open Wilson lines tend to form closed Wilson loops at high energy.

Cyclic symmetry of Wilson lines is crucial for accurate correlation function computation.

Implications for string theory calculations of Wilson line correlators are discussed.

Abstract

We investigate the high energy behavior of the correlation functions of the open Wilson lines in noncommutative gauge theory. We obtain a very simple physical picture that they are bound to form a group of closed Wilson loops. We prove our claim in the weak coupling region by perturbative analysis. We emphasize the importance of respecting the cyclic symmetry of the straight Wilson lines to compute the correlation functions. The implications for stringy calculation of the correlators are also discussed.