Dirac spectrum representation of Polyakov loop fluctuations in lattice QCD

TL;DR

This paper derives a Dirac spectrum representation for Polyakov loop fluctuations in lattice QCD, revealing that low-lying Dirac modes minimally influence these fluctuations and challenging the direct link between confinement and chiral symmetry breaking.

Contribution

The study introduces a novel analytical relation for Polyakov loop fluctuations using Dirac spectrum on odd-length lattices, combining semi-analytical and numerical methods.

Findings

Low-lying Dirac eigenmodes have minimal impact on Polyakov loop fluctuations.

Polyakov loop fluctuations are sensitive probes for quark deconfinement.

Results suggest no direct one-to-one correspondence between confinement and chiral symmetry breaking.

Abstract

Dirac spectrum representations of the Polyakov loop fluctuations are derived on the temporally odd-number lattice, where the temporal length is odd with the periodic boundary condition. We investigate the Polyakov loop fluctuations based on these analytical relations. It is semianalytically and numerically found that the low-lying Dirac eigenmodes have little contribution to the Polyakov loop fluctuations, which are sensitive probe for the quark deconfinement. Our results suggest no direct one-to-one corresponding between quark confinement and chiral symmetry breaking in QCD.