The Vortex Structure of SU(2) Calorons

TL;DR

This paper investigates the vortex structures within SU(2) calorons using gauge fixing methods, revealing their connection to confinement mechanisms and the influence of holonomy on vortex behavior.

Contribution

It demonstrates the detailed vortex structure of SU(2) calorons and their role in the vortex confinement scenario, highlighting the dependence on holonomy and the percolation of vortices.

Findings

Vortices in calorons connect dyons and depend on holonomy.

Spatial vortices percolate when holonomy is maximally nontrivial.

Calorons facilitate the vortex confinement mechanism.

Abstract

We reveal the center vortex content of SU(2) calorons and ensembles of them. We use Laplacian Center Gauge as well as Maximal Center Gauges to show that the vortex in a single caloron consists of two parts. The first one connects the constituent dyons of the caloron (which are monopoles in Laplacian Abelian Gauge) and extends in time. The second part is predominantly spatial, encloses one of the dyons and can be related to the twist in the caloron gauge field. This part depends strongly on the caloron holonomy and degenerates to a plane when the holonomy is maximally nontrivial, i.e. when the asymptotic Polyakov loop is traceless. Correspondingly, we find the spatial vortices in caloron ensembles to percolate in this case. This finding fits perfectly in the confinement scenario of vortices and shows that calorons are suitable to facilitate the vortex confinement mechanism.