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

Abstract

We propose that the Higgs phase of a gauge Higgs theory is the phase of spontaneously broken custodial symmetry, and present a new gauge invariant order parameter for custodial symmetry breaking which is very closely analogous to the Edwards-Anderson order parameter for spin glasses. Custodial symmetry is a global symmetry acting on the Higgs field alone, and we show here that the spin glass transition in gauge Higgs theories, from a QCD-like phase to a Higgs phase of broken custodial symmetry, coincides with the transition between two distinct 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.

arXiv comment17 pages, 1 figure

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• Numerical indication that center vortices drive dynamical mass generation in QCD
• Excited states of massive fermions in a chiral gauge theory
• Confinement-Higgs and deconfinement-Higgs transitions in three-dimensional $Z(2)$ LGT
• The Higgs phase as a spin glass phase in D=5 dimensional SU(2) gauge Higgs theory
• Gauge-independent transition separating confinement and Higgs phases in lattice SU(2) gauge theory with a scalar field in the fundamental representation
• Quantum excitations of static charges in the Ginzburg-Landau model of superconductivity