Removal of Z_3-symmetry breaking from Fermionic Determinants

TL;DR

This paper investigates methods to eliminate Z_3-symmetry breaking effects in fermionic determinants to better understand the confining nature of the quantum vacuum, proposing new order parameters and testing their effectiveness.

Contribution

It introduces prescriptions that avoid charge-screening effects, compares two order parameters, and demonstrates the suitability of fermionic determinants for studying vacuum confinement.

Findings

Fermionic determinants show small fluctuations compared to Polyakov loops.

Fermionic determinants reflect vacuum characteristics more reliably.

Prescriptions can clarify confinement properties without charge-screening effects.

Abstract

We consider prescriptions that are free from the direct charge-screening effects by quark loops and enable us to clarify the confining nature of a vacuum. We test two candidates for an order parameter, a Polyakov loop ($P$) evaluated in zero-triality backgrounds and fermionic determinants (${\mathcal D}_{1,2}$) with non-zero triality. Especially, ${\mathcal D}_{1,2}$ has very small fluctuations in comparison with a Polyakov loop in zero-triality sector, and seems to well reflect the characteristic of a vacuum. Such prescriptions could be still usable for the clarification of the confinement property of a vacuum.