  We show that the Higgs and confinement phases of a gauge Higgs theory, with
the Higgs field in the fundamental representation of the gauge group, are
distinguished both by a broken or unbroken realization of the global center
subgroup of the gauge group, and by the type of confinement in each phase. This
is color confinement in the Higgs phase, and a stronger property, which we call
"separation-of-charge" confinement, in the confining phase.
