New numerical results and novel effective string predictions for Wilson loops

TL;DR

This paper computes three-loop predictions of the Nambu-Goto effective string model for Wilson loops and tests these predictions against Monte Carlo simulations in the 3D Ising gauge model, finding partial agreement.

Contribution

It provides the first three-loop calculation for Wilson loops using an operatorial approach and tests these predictions with high-precision Monte Carlo simulations.

Findings

Two-loop corrections are confirmed by simulations.

Three-loop effects are consistent with predictions but not statistically significant.

Universality theorems support the three-loop predictions across models.

Abstract

We compute the prediction of the Nambu-Goto effective string model for a rectangular Wilson loop up to three loops. This is done through the use of an operatorial, first order formulation and of the open string analogues of boundary states. This result is interesting since there are universality theorems stating that the predictions up to three loops are common to all effective string models. To test the effective string prediction, we set up the Montecarlo evaluation, in the 3d Ising gauge model, of an observable (the ratio of two Wilson loops with the same perimeter) for which boundary effects are relatively small. Our simulation attains a level of precision which is sufficient to test the two-loop correction. The three-loop correction seems to go in the right direction, but is actually yet beyond the reach of our simulation, since its effect is comparable with the statistical errors of the latter.