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

TL;DR

This paper derives an analytical relation connecting the Polyakov loop and Dirac modes on a specific lattice, revealing that low-lying Dirac modes minimally influence confinement and chiral symmetry breaking, challenging their direct correlation.

Contribution

It introduces a new analytical relation on a temporally odd lattice and numerically investigates Dirac mode contributions to the Polyakov loop in QCD phases.

Findings

Low-lying Dirac modes have little impact on the Polyakov loop.

No direct one-to-one correspondence between confinement and chiral symmetry breaking.

A new positive/negative symmetry in Dirac-mode matrix elements appears in the confinement phase.

Abstract

The Polyakov loop and the Dirac modes are connected via a simple analytical relation on the temporally odd-number 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.