Ultraviolet divergences in the cyclic Wilson loop and their renormalization

TL;DR

This paper analyzes the ultraviolet divergences of the cyclic Wilson loop, revealing that it has intersection divergences instead of cusp divergences, and discusses its renormalization properties in the context of quantum field theory.

Contribution

It identifies the unique divergence structure of the cyclic Wilson loop and shows how to renormalize it by comparing with Polyakov loop correlators.

Findings

Cyclic Wilson loop exhibits intersection divergences, not cusp divergences.

The cyclic Wilson loop is not multiplicatively renormalizable on its own.

The difference between the cyclic Wilson loop and Polyakov loop correlator is renormalizable.

Abstract

We discuss the cyclic Wilson loop, i.e. a rectangular Wilson loop that spans the entire compactified time axis in the imaginary time formalism. The result of a perturbative calculation at $O(\alpha_s^2)$ is given, with the main focus on the ultraviolet divergences of this operator. Based on a general analysis of divergences in loop diagrams, we find that, unlike usual Wilson loops, the cyclic loop does not have cusp divergences but intersection divergences, where the intersections arise due to the periodic boundary conditions. As a result, the cyclic Wilson loop itself is not multiplicatively renormalizable, but the difference between it and the correlator of two Polyakov loops is.