Lattice QCD study of confinement and chiral symmetry breaking with Dirac-mode expansion

TL;DR

This study uses a gauge-covariant Dirac-mode expansion in lattice QCD to analyze the relationship between confinement and chiral symmetry breaking, revealing they are not directly correlated.

Contribution

The paper introduces a novel gauge-covariant Dirac-mode expansion method to analyze confinement and chiral symmetry breaking in lattice QCD.

Findings

Confinement persists even after removing low-lying Dirac modes.

The Polyakov loop remains near zero without low-lying modes, indicating unbroken confinement.

Chiral symmetry breaking and confinement are not directly linked.

Abstract

Using the eigen-mode of the QCD Dirac operator $\Slash D=\gamma^\mu D^\mu$, we develop a manifestly gauge-covariant expansion and projection of the QCD operators such as the Wilson loop and the Polyakov loop. With this method, we perform a direct analysis of the correlation between confinement and chiral symmetry breaking in lattice QCD Monte Carlo calculations. Even after removing the low-lying Dirac modes, which are responsible to chiral symmetry breaking, we find that the Wilson loop obeys the area law, and the string tension or the confinement force is almost unchanged. 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.