Dirac-mode expansion for confinement and chiral symmetry breaking

Abstract

We develop a manifestly gauge-covariant expansion and projection using the eigen-mode of the QCD Dirac operator / D= γ μ D μ . Applying this method to the Wilson loop and the Polyakov loop, we perform a direct analysis of the correlation between confi nement and chiral symmetry breaking in SU(3) lattice QCD calculation on 6 4 at β =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 remo ving the low-lying Dirac modes, which are responsible to chiral symmetry breaking. We find al so that the Polyakov loop remains to be almost zero even without the low-lying Dirac modes, which indicates the Z3-unbroken confinement phase. These results indicate that one-to-one c orrespondence does not hold between confinement and chiral symmetry breaking in QCD.