Abstract
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.
Highlights
The second question is: What is meant by the word “confinement” in a theory with matter in the fundamental representation of the gauge group? In such theories, the order parameters associated with pure gauge theories, i.e., non-vanishing string tension, ‘t Hooft loops, Polyakov loops, and vortex free energies have apparently non-confining behavior
Since our discussion has focused on gauge Higgs theory, it is natural to ask how it applies to a theory like QCD, where the matter in the fundamental representation of the gauge group is fermionic, and we would expect that the global center subgroup of the gauge group is unbroken
We have argued that, contrary to the general consensus, there really is an essential distinction to be made between the confinement and Higgs phases of a gauge Higgs theory, and that these phases are distinguished by confinement type, and by the broken or unbroken realization of a global center subgroup of the gauge group
Summary
Starting with the first question, most discussions of the Higgs mechanism begin with a “Mexican hat” potential of some kind, and the Higgs field is expanded around one of the minima φ0 of this potential, i.e., φ(x) = φ0 + δφ(x), where the particular minimum is selected by fixing to a unitary gauge. This is perfectly consistent with Elitzur’s theorem, and some textbooks and review articles (e.g., [7,8]) do define “spontaneous gauge symmetry breaking” in this way. The problem with this idea is that the location of the transition line is gauge-dependent [9].
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