Polyakov Loop Fluctuations in Terms of Dirac Eigenmodes

Abstract

We investigate, both numerically and analytically, the Polyakov loop and its fluctuations in terms of Dirac eigenmodes in the lattice QCD. Based on the analytical relation between the Polyakov loop and the Dirac eigenmodes, it is found that the Polyakov loop and its fluctuations, contrary to the chiral condensate, are insensitive to the density of the low-lying Dirac modes. This result suggests that there is no direct one-to-one correspondence between quark confinement and chiral symmetry breaking in QCD. Our argument is also generalized for the Wilson-type Dirac operator on the lattice.