Lattice QCD analysis for relation between quark confinement and chiral symmetry breaking

Abstract

The Polyakov loop and the Dirac modes are connected via a simple analytical relation on the temporally oddnumber lattice, where the temporal lattice size is odd with the normal (nontwisted) periodic boundary condition. Using this relation, we investigate the relation between quark confinement and chiral symmetry breaking in QCD. In this paper, we discuss the properties of this analytical relation and numerically investigate each Dirac-mode contribution to the Polyakov loop in both confinement and deconfinement phases at the quenched level. This relation indicates that low-lying Dirac modes have little contribution to the Polyakov loop, and we numerically confirmed this fact. From our analysis, it is suggested that there is no direct one-to-one corresponding between quark confinement and chiral symmetry breaking in QCD. Also, in the confinement phase, we numerically find that there is a new "positive/negative symmetry" in the Dirac-mode matrix elements of link-variable operator which appear in the relation and the Polyakov loop becomes zero because of this symmetry. In the deconfinement phase, this symmetry is broken and the Polyakov loop is non-zero.

Selected issues in thermal field theory

“…An intriguing question is whether confinement would also be lost if the Dirac zero modes are artificially removed from a system. In [8,9,10,11,12], a relation of the Dirac eigenmodes to the Polyakov loop has been formulated on a lattice, and their dynamical correlations have been investigated in SU(3) lattice gauge theory. The expression in a gauge-invariant formalism is found as [11,12] …”