Renormalization of the cyclic Wilson loop

TL;DR

This paper investigates the ultraviolet divergence in the cyclic Wilson loop at finite temperature, revealing it stems from self-intersection due to periodic boundary conditions, and explores its renormalization and implications for lattice QCD and quarkonium studies.

Contribution

It demonstrates that the divergence arises from self-intersection, not cusps, and establishes a renormalization framework involving Polyakov loop correlators, extending understanding of cyclic Wilson loops.

Findings

Divergence linked to self-intersection, not cusps.

Renormalization involves mixing with Polyakov loop correlators.

Resummation of leading logarithms improves theoretical predictions.

Abstract

In finite-temperature field theory, the cyclic Wilson loop is defined as a rectangular Wilson loop spanning the whole compactified time direction. In a generic non-abelian gauge theory, we calculate the perturbative expansion of the cyclic Wilson loop up to order g^4. At this order and after charge renormalization, the cyclic Wilson loop is known to be ultraviolet divergent. We show that the divergence is not associated with cusps in the contour but is instead due to the contour intersecting itself because of the periodic boundary conditions. One consequence of this is that the cyclic Wilson loop mixes under renormalization with the correlator of two Polyakov loops. The resulting renormalization equation is tested up to order g^6 and used to resum the leading logarithms associated with the intersection divergence. Implications for lattice studies of this operator, which may be relevant for the phenomenology of quarkonium at finite temperature, are discussed.