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

Abstract

In SUðNÞ 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 ¼ 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.

On the observable spectrum of theories with a Brout–Englert–Higgs effect

“…We thus assume that considering operators of the described classes do indeed describe localizable particles and are sufficient to describe all particle-like excitations in any given quantum number channel. Concerning the status for other operator classes in theories of the type considered here, we refer to [37,38] for recent investigations.…”

On the distinction between color confinement, and confinement

“…For a more extensive presentation of the work summarized here, please see refs. [6,8]. Figure 7: For SU(2) gauge-Higgs theory, C confinement exists above the line denoted "Dirac," and S c confinement exists in a strong-coupling region, as well as along the line at β = 0.…”

“…This is based on strong-coupling expansions and the Gershgorim Theorem in linear algebra. The argument is, however, a little lengthy, and for that we must refer the reader to section VI in our article [6]. The second question is whether S c confinement holds everywhere in the β − γ phase diagram.…”

Different Faces of Confinement

“…A clear symmetry-based distinction between the confining and Higgs phases in a gauge theory with fundamental representation matter fields has been recently proposed in Refs. [110,280,281]. An important generalised criterion of confinement valid in both pure YM theories and YM theories with matter in the fundamental representation states that…”

“…In Refs. [110,280,281], it has been shown that a transition between the Cand S c -confinement phases must take place in the gauge-Higgs theory, and the unbroken custodial symmetry has been found to separate the S c -confining (if not massless) phase from the Higgs phase corresponding to a C-confined spin glass state, where the custodial symmetry is actually broken. It would be very interesting to see how such a new concept of S c -confinement can be applied for more realistic theories such as QCD.…”