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We propose that the Higgs phase of a gauge Higgs theory is the phase ofspontaneously broken custodial symmetry, and present a new gauge invariantorder parameter for custodial symmetry breaking which is very closely analogousto the Edwards-Anderson order parameter for spin glasses. Custodial symmetry isa global symmetry acting on the Higgs field alone, and we show here that thespin glass transition in gauge Higgs theories, from a QCD-like phase to a Higgsphase of broken custodial symmetry, coincides with the transition between twodistinct types of confinement. These are color confinement in the Higgs phase,and a stronger version of confinement, which we have termed"separation-of-charge" confinement, in the QCD-like phase.

The Higgs phase as a spin glass, and the transition between varieties of confinement