  All colored particles including dynamical quarks and gluons are confined if
the color confinement criterion proposed by Kugo and Ojima is satisfied. The
criterion was obtained under the gauge fixing of the Lorenz type. However, it
was pointed out that the Kugo-Ojima criterion breaks down for the Maximal
Abelian gauge, which is quite strange in view of the fact that quark
confinement has been verified according to the dual superconductivity caused by
magnetic monopole condensations. In order to make a bridge between color
confinement due to Kugo and Ojima and the dual superconductor picture for quark
confinement, we investigate a generalization of the color confinement criterion
to obtain the unified picture for confinement. We show that the restoration of
the residual local gauge symmetry which was shown in the Lorenz gauge by Hata
to be equivalent to the Kugo-Ojima criterion indeed occurs in the Maximal
Abelian gauge for the SU(N) Yang-Mills theory in two-, three- and
four-dimensional Euclidean spacetime once the singular topological
configurations of gauge fields are taken into account. This result indicates
that the color confinement phase is a disordered phase caused by non-trivial
topological configurations irrespective of the gauge choice. As a byproduct, we
show that the compact U(1) gauge theory can have the disordered confinement
phase, while the non-compact U(1) gauge theory has the deconfined Coulomb
phase.
