Vortices in the SU(2)-Higgs model -- Vortices and the covariant adjoint Laplacian

TL;DR

This paper investigates the role of vortices in the SU(2)-Higgs model, showing their behavior in different phases and proposing methods to identify vortices using the covariant adjoint Laplacian, with implications for understanding confinement.

Contribution

It demonstrates that eigenvectors of the covariant adjoint Laplacian can identify vortices in certain gauge configurations and discusses modifications needed for Monte Carlo data.

Findings

Vortices are suppressed in the Higgs phase but persist in the confined phase.

Eigenvectors of the covariant adjoint Laplacian can locate vortices in specific configurations.

Modified approaches are necessary to identify vortices in Monte Carlo generated configurations.

Abstract

Vortices in the SU(2)--Higgs model: The presence of a fundamental Higgs in the SU(N)-Higgs model yields color screening at some finite distance. Whereas the transition to the Higgs "phase" is accompanied by a suppression of projected center vortices, there is nearly no influence of color screening on the vortex properties in the confined "phase". Hence the behavior of the Wilson loop can be described in both phases within the vortex picture of confinement. Vortices and the covariant adjoint Laplacian: Laplacian center gauge is a method to localize center vortices in SU(N) gauge theory. We show that the eigenvectors of the covariant adjoint Laplacian identify vortices for a special class of gauge field configurations. However, for Monte Carlo generated configurations, modified approaches are required.