Abstract
According to recent work of Greensite and Matsuyama, the Higgs phase of a gauge Higgs theory is distinguished from the confinement and massless phases by the spontaneous breaking of a global center subgroup of the gauge group, and by confinement type. This is contrary to the notion that there is no essential distinction between the Higgs and confinement phases when the Higgs field is in the fundamental representation of the gauge group. Although this new symmetry breaking order parameter has been investigated in $D=4$ dimensions, there is so far no check in a non-abelian gauge theory containing a massless as well as confinement/Higgs phases, where the prediction is that the symmetry breaking order parameter will show transition lines separating the massless to Higgs and confinement to Higgs phases, but not the massless to confinement phase. In this work we map out the phase structure of the $D=5$ dimensional model, according to both the symmetry breaking parameter and thermodynamic observables, and check the assertion regarding the massless to confinement phase.
Highlights
One often hears that there is no true distinction between the Higgs and confinement phases of a gauge-Higgs theory, when the Higgs field is in the fundamental representation of the gauge group
There is the work of Osterwalder and Seiler [1], Banks and Rabinovici [2], and Fradkin and Shenker [3], which tells us that the Higgs and confinement phases cannot be entirely isolated from one another in the phase diagram by a thermodynamic transition
An investigation of lattice SU(2) gauge-Higgs theory in D 1⁄4 5 dimensions confirms an important, and up to now untested, assertion of the proposed identification of the Higgs phase as a phase in which the global center subgroup of the gauge group is spontaneously broken. This identification presupposes that the massless phase and the confinement phase are both phases of unbroken symmetry
Summary
One often hears that there is no true distinction between the Higgs and confinement phases of a gauge-Higgs theory, when the Higgs field is in the fundamental representation of the gauge group. There is no obvious gauge-invariant order parameter, such as a Polyakov line, which would distinguish the two phases. It is known from Elitzur’s theorem that a local symmetry cannot break spontaneously, and it seems erroneous to describe the Higgs phase as a phase of spontaneously broken gauge symmetry. The asymptotic particle states of, e.g., an SU(2) gauge-Higgs theory are created by local color singlet operators, in both the Higgs and confinement regions of the phase diagram [2,4,5].
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