What symmetry is actually broken in the Higgs phase of a gauge-Higgs theory?

Abstract

In SU($N$) gauge-Higgs theories, with a single Higgs field in the fundamental representation, there exists in addition to the local gauge symmetry a global SU(2) symmetry, at $N=2$, and a global U(1) symmetry, for $N\ne 2$. We construct a gauge-invariant order parameter for the breaking of these global symmetries in the Higgs sector, and calculate numerically the transition lines, in coupling-constant space, for SU(2) and SU(3) gauge theories with unimodular Higgs fields. The order parameter is non-local, and therefore its non-analyticity does not violate the theorem proved by Osterwalder and Seiler. We then show that there exists a transition, in gauge-Higgs theories, between two types of confinement: ordinary color neutrality in the Higgs region, and a stronger condition, which we have called "separation-of-charge confinement," in the confinement region. We conjecture that the symmetry-breaking transition coincides with the transition between these two physically different types of confinement.

20 pages, 14 figures. v2: new section VII, other minor revisions. Version to appear in PRD

References in corpus (3)

• On the Ambiguity of Spontaneously Broken Gauge Symmetry
• A confinement criterion for gauge theories with matter fields
• Predicting the singlet vector channel in a partially Higgsed gauge theory

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• Analytical relations for the bound state spectrum of gauge theories with a Brout-Englert-Higgs mechanism
• Centre vortex structure in the presence of dynamical fermions
• Different faces of confinement
• The nature of symmetry breaking in the superconducting ground state
• Higgs-confinement continuity and matching of Aharonov-Bohm phases
• Numerical indication that center vortices drive dynamical mass generation in QCD
• Confinement-Higgs and deconfinement-Higgs transitions in three-dimensional $Z(2)$ LGT
• Gauge-independent transition separating confinement and Higgs phases in lattice SU(2) gauge theory with a scalar field in the fundamental representation