Polyakov loop fluctuations in Dirac eigenmode expansion

TL;DR

This study explores the relationship between Polyakov loop fluctuations and Dirac eigenmodes in lattice QCD, revealing that low-lying modes minimally influence these fluctuations, thus challenging the direct link between confinement and chiral symmetry breaking.

Contribution

The paper derives analytic relations between Polyakov loop fluctuations and Dirac eigenmodes on a specific lattice and confirms their negligible correlation through numerical simulations in SU(3) QCD.

Findings

Low-lying Dirac modes have negligible impact on Polyakov loop fluctuations.

The results hold in both confined and deconfined phases.

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

Abstract

We investigate correlations of the Polyakov loop fluctuations with eigenmodes of the lattice Dirac operator. Their analytic relations are derived on the temporally odd-number size lattice with the normal non-twisted periodic boundary condition for the link-variables. We find that the low-lying Dirac modes yield negligible contributions to the Polyakov loop fluctuations. This property is confirmed to be valid in confined and deconfined phase by numerical simulations in SU(3) quenched QCD. These results indicate that there is no direct, one-to-one correspondence between confinement and chiral symmetry breaking in QCD in the context of different properties of the Polyakov loop fluctuation ratios.