Smoothing algorithms for projected center-vortex gauge fields

TL;DR

This paper introduces novel smoothing techniques for Z(3)-projected center-vortex gauge fields, including centrifuge preconditioning and vortex-preserved annealed smoothing, to effectively smooth vortex configurations while maintaining their core structure.

Contribution

The paper presents new preconditioning and annealed smoothing methods specifically designed for vortex gauge fields, addressing limitations of naive smoothing techniques.

Findings

Successfully achieved smooth vortex fields with preserved structures

Enhanced the effectiveness of smoothing in vortex studies

Provided a framework for advanced operator analysis on vortex configurations

Abstract

We study the application of $\mathrm{SU}(3)$ gauge field smoothing methods to $\mathrm{Z}(3)$-projected center-vortex gauge fields. Due to the proportionality of the vortex links to the identity, naive applications of these methods are either ineffectual or limited in scope, containing subtle issues which are not obviously manifest. To overcome these issues we introduce centrifuge preconditioning, a novel method applied prior to smoothing that rotates the links away from the center while preserving the fundamental structure of the vortex field. Additionally, the concept of vortex-preserved annealed smoothing is formulated to ensure the smoothing procedure maintains the underlying vortex structure. The application of these new methods in the context of annealed smoothing applied to vortex fields is shown to successfully achieve the desired smoothness condition required for the study of more advanced operators.