Dirac-mode expansion analysis for Polyakov loop

TL;DR

This study investigates how Dirac eigenmodes influence the Polyakov loop in SU(3) lattice QCD, revealing that the Polyakov loop remains unaffected by the removal of low-lying or UV Dirac-modes, thus clarifying the relation between chiral symmetry breaking and confinement.

Contribution

It demonstrates that the Polyakov loop's behavior is insensitive to the removal of low-lying or UV Dirac-modes, providing new insights into the connection between chiral symmetry breaking and confinement.

Findings

Polyakov loop remains near zero in confined phase despite Dirac-mode cuts.

Polyakov loop behavior is unchanged by Dirac-mode removal in deconfined phase.

Chiral symmetry breaking and confinement are not directly linked through Dirac eigenmodes.

Abstract

To clarify the relation between chiral symmetry breaking and color confinement, we investigate the Polyakov loop in terms of the Dirac eigenmodes in SU(3) lattice QCD. We analyze the low-lying (IR) and UV Dirac-mode contribution to the Polyakov loop, respectively, using the Dirac-mode expansion method. In the confined phase, the Polyakov loop $< L_P >$ remains almost zero and $Z_3$ center symmetry is thus unbroken, even after removing low-lying Dirac-modes, which are responsible to chiral symmetry breaking. In the confined phase, the Polyakov loop $< L_P >$ also remains almost zero by UV Dirac-modes cut. In addition to the confined phase, we analyze the Polyakov loop in the deconfined phase and its temperature dependence. The behavior of the Polyakov loop $< L_P >$ is found to be almost unchanged by the cut of low-lying or UV Dirac-modes in both confined and deconfined phases.