  We analytically study the relation between quark confinement and spontaneous
chiral-symmetry breaking in QCD. In terms of the Dirac eigenmodes, we derive
some formulae for the Polyakov loop, its fluctuations, and the string tension
from the Wilson loop. We also investigate the Polyakov loop in terms of the
eigenmodes of the Wilson, the clover and the domain wall fermion kernels,
respectively. For the confinement quantities, the low-lying Dirac/fermion
eigenmodes are found to give negligible contribution, while they are essential
for chiral symmetry breaking. These relations indicate no direct one-to-one
correspondence between confinement and chiral symmetry breaking in QCD, which
seems to be natural because confinement is realized independently of the quark
mass.
