Some Relations for Quark Confinement and Chiral Symmetry Breaking in QCD

TL;DR

This paper analytically explores the relationship between quark confinement and chiral symmetry breaking in QCD, revealing that low-lying Dirac eigenmodes are crucial for chiral symmetry but not for confinement, indicating these phenomena are not directly linked.

Contribution

The study derives new formulae connecting Dirac eigenmodes with confinement indicators and shows the independence of confinement from chiral symmetry breaking in QCD.

Findings

Low-lying Dirac eigenmodes are negligible for confinement quantities.

Chiral symmetry breaking depends on low-lying Dirac modes.

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

Abstract

We analytically study the relation between quark confinement and spontaneous chiral-symmetry breaking in QCD. In terms of the Dirac eigenmodes, we derive some formulae for the Polyakov loop, its fluctuations, and the string tension from the Wilson loop. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clover and the domain wall fermion kernels, respectively. For the confinement quantities, the low-lying Dirac/fermion eigenmodes are found to give negligible contribution, while they are essential for chiral symmetry breaking. These relations indicate no direct one-to-one correspondence between confinement and chiral symmetry breaking in QCD, which seems to be natural because confinement is realized independently of the quark mass.