Dirac-mode expansion for confinement and chiral symmetry breaking

TL;DR

This paper introduces a gauge-covariant Dirac eigen-mode expansion to analyze confinement and chiral symmetry breaking in lattice QCD, revealing they are not directly correlated.

Contribution

It develops a novel Dirac-mode expansion method and applies it to demonstrate the independence of confinement and chiral symmetry breaking in SU(3) lattice QCD.

Findings

Wilson loop obeys the area law even after removing low-lying Dirac modes

String tension remains almost unchanged without low-lying Dirac modes

Polyakov loop stays near zero, indicating unbroken confinement phase without low-lying modes

Abstract

We develop a manifestly gauge-covariant expansion and projection using the eigen-mode of the QCD Dirac operator. Applying this method to the Wilson loop and the Polyakov loop, we perform a direct analysis of the correlation between confinement and chiral symmetry breaking in SU(3) lattice QCD calculation on 6^4 at beta=5.6 at the quenched level. Notably, the Wilson loop is found to obey the area law, and the slope parameter corresponding to the string tension or the confinement force is almost unchanged, even after removing the low-lying Dirac modes, which are responsible to chiral symmetry breaking. We find also that the Polyakov loop remains to be almost zero even without the low-lying Dirac modes, which indicates the Z_3-unbroken confinement phase. These results indicate that one-to-one correspondence does not hold between confinement and chiral symmetry breaking in QCD.