Polyakov loop analysis with Dirac-mode expansion

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.