Gauge-Invariant Formalism with Dirac-mode Expansion for Confinement and Chiral Symmetry Breaking

Physics – High Energy Physics – High Energy Physics - Lattice

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Scientific paper

We develop a manifestly gauge-covariant expansion of the QCD operator such as the Wilson loop, using the eigen-mode of the QCD Dirac operator $\Slash D=\gamma^\mu D^\mu$. With this method, we perform a direct analysis of the correlation between confinement and chiral symmetry breaking in lattice QCD Monte Carlo calculation on $6^4$ at $\beta$=5.6. As a remarkable fact, the confinement force is almost unchanged even after removing the low-lying Dirac modes, which are responsible to chiral symmetry breaking. This indicates that one-to-one correspondence does not hold for between confinement and chiral symmetry breaking in QCD. In this analysis, we carefully amputate only the "essence of chiral symmetry breaking" by cutting off the low-lying Dirac modes, and can artificially realize the "confined but chiral restored situation" in QCD.

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