1202.4130 (Shinya Gongyo et al.)

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

Shinya Gongyo, Takumi Iritani, Hideo Suganuma

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.

View original: http://arxiv.org/abs/1202.4130