Polyakov loop analysis with Dirac-mode expansion

TL;DR

This study explores the relationship between confinement and chiral symmetry breaking in QCD by analyzing the Polyakov loop through Dirac eigenmodes, revealing that confinement persists regardless of low-lying or high Dirac-modes.

Contribution

It introduces a Dirac-mode expansion method in lattice QCD to analyze the Polyakov loop's dependence on Dirac eigenmodes in both phases.

Findings

Polyakov loop remains near zero below T_c even after removing low-lying Dirac-modes.

Polyakov loop behavior is insensitive to Dirac-modes above T_c.

Chiral condensate is reduced when low-lying Dirac-modes are removed, but confinement persists.

Abstract

In order to investigate the direct relation between confinement and chiral symmetry breaking in QCD, we investigate the Polyakov loop in terms of the Dirac eigenmodes in both confined and deconfined phases. Using the Dirac-mode expansion method in SU(3) lattice QCD, we analyze the contribution of low-lying and higher Dirac-modes to the Polyakov loop, respectively.In the confined phase below T_c, after removing low-lying Dirac-modes, the chiral condensate $< \bar{q} q>$ is largely reduced, however, the Polyakov loop remains almost zero and Z_3-center symmetry is unbroken. These results indicate that the system is still in the confined phase without low-lying Dirac-modes. By higher Dirac-modes cut, the Polyakov loop also remains almost zero below T_c. We also analyze the Polyakov loop in the deconfined phase above T_c. We find that the Polyakov loop and Z_3-symmetry behavior are insensitive to low-lying and higher Dirac-modes in both confined and deconfined phases.