## Lattice QCD analysis of the Polyakov loop in terms of Dirac eigenmodes: Relation between confinement and chiral symmetry breaking    [PDF]

Takumi Iritani, Hideo Suganuma
Using the Dirac-mode expansion method, which keeps the gauge invariance, we analyze the Polyakov loop in terms of the Dirac modes in SU(3) quenched lattice QCD in both confined and deconfined phases. First, to investigate the direct correspondence between confinement and chiral symmetry breaking, we remove low-lying Dirac-modes from the confined vacuum generated by lattice QCD. In this system without low-lying Dirac modes, while the chiral condensate $< \bar{q}q >$ is extremely reduced, we find that the Polyakov loop is almost zero and Z_3-center symmetry is unbroken, which indicates quark confinement. We also investigate the removal of ultraviolet (UV) Dirac-modes, and find that the Polyakov loop is almost zero. Second, we deal with the deconfined phase above T_c, and find that the behaviors of the Polyakov loop and Z_3-symmetry are not changed without low-lying or UV Dirac-modes. Finally, we develop a new method to remove low-lying Dirac modes from the Polyakov loop for a larger lattice of 12^3 $\times$ 4 at finite temperature, and find almost the same results. These results suggest that there is no direct correspondence between confinement and chiral symmetry breaking through Dirac-eigenmodes.
View original: http://arxiv.org/abs/1305.4049