Properties of canonical fermion determinants with a fixed quark number

TL;DR

This study investigates the properties of canonical fermion determinants in lattice QCD, revealing strong signatures of center symmetry breaking above the transition temperature and analyzing quark sector weights.

Contribution

The paper introduces a dimensional reduction approach to analyze canonical determinants and explores their behavior across the QCD transition temperature.

Findings

Signatures of center symmetry breaking are prominent above T_c.

Canonical determinants' distribution in the complex plane reflects symmetry breaking.

The relative weights of quark sectors vary significantly across the transition.

Abstract

Using a dimensional reduction formula for the lattice fermion determinant we study canonical determinants on quenched SU(3) gauge configurations. The canonical determinants decribe a fixed quark number and we analyze their properties below and above the transition temperature. We find that above $T_c$ the signatures of center symmetry breaking are very strongly manifest in the distribution of the canonical determinants in the complex plane, and we discuss possible physical implications of this finding. We furthermore analyze the relative weight of the different quark sectors below and above the transition temperature.