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

摘要

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 ≠ 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 nonlocal, and, therefore, its nonanalyticity 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.