Scaling properties of Wilson loops pierced by P-vortices

TL;DR

This study investigates the scaling behavior of Wilson loops linked to P-vortices in SU(2) lattice gauge theory, revealing consistent scaling properties and insensitivity to vortex piercing points.

Contribution

It demonstrates that the ratio of linked to unlinked Wilson loops exhibits approximate scaling and is insensitive to the vortex piercing point, providing insights into P-vortex properties.

Findings

Ratios of linked to unlinked Wilson loops scale consistently across lattice couplings.

Ratios are insensitive to the minimal area point pierced by P-vortices.

Results support the scaling hypothesis for P-vortex linked Wilson loops.

Abstract

P-vortices, in an SU(N) lattice gauge theory, are excitations on the center-projected Z(N) lattice. We study the ratio of expectation values of SU(2) Wilson loops, on the unprojected lattice, linked to a single P-vortex, to that of Wilson loops which are not linked to any P-vortices. When these ratios are plotted versus loop area in physical units, for a range of lattice couplings, it is found that the points fall approximately on a single curve, consistent with scaling. We also find that the ratios are rather insensitive to the point where the minimal area of the loop is pierced by the P-vortex.