Investigation of the ensemble of maximal center gauge

TL;DR

This paper explores the ensemble of local maxima in Maximal Center Gauge to improve vortex detection and address the underestimation of string tension in gauge functional maximization.

Contribution

It introduces a restricted maximization approach within the ensemble of local maxima to better estimate the string tension in Maximal Center Gauge.

Findings

Restricted maximization reduces string tension underestimation.

Ensemble analysis improves vortex detection accuracy.

Gaussian-based restriction enhances gauge functional maximization.

Abstract

Maximal Center Gauge (MCG) aims to detect center vortices by maximizing a gauge functional and then projecting onto the center elements of the respective group. The requirement for unrestricted maximization of the gauge functional has proven to be untenable because it was shown that it leads to an underestimation of the string tension. To counter this problem, the ensemble of local gauge maxima is investigated and it is found that the unrestricted maximization can be replaced by a maximization restricted to the Gaussian distributed part of the ensemble. Such restricted maximization weakens the problem of an underestimated string tension.