Zero Point Energy of Renormalized Wilson Loops

TL;DR

This paper investigates the zero point energy of the quark-antiquark potential via Wilson loops, introducing a renormalization method that eliminates perturbative contributions and exploring nonperturbative effects through effective string models.

Contribution

It presents a unique renormalization prescription for Wilson loops that nullifies perturbative zero point energy and analyzes nonperturbative contributions using effective string theories.

Findings

Perturbative zero point energy vanishes with the new renormalization.

Nonperturbative zero point energy is zero in the Nambu model.

One-loop nonperturbative contribution is negative regardless of extrinsic curvature.

Abstract

The quark antiquark potential, and its associated zero point energy, can be extracted from lattice measurements of the Wilson loop. We discuss a unique prescription to renormalize the Wilson loop, for which the perturbative contribution to the zero point energy vanishes identically. A zero point energy can arise nonperturbatively, which we illustrate by considering effective string models. The nonperturbative contribution to the zero point energy vanishes in the Nambu model, but is nonzero when terms for extrinsic curvature are included. At one loop order, the nonperturbative contribution to the zero point energy is negative, regardless of the sign of the extrinsic curvature term.