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

TL;DR

This paper investigates the nature of symmetry breaking in gauge-Higgs theories, introducing a gauge-invariant order parameter, and explores the transition between different confinement regimes in SU(N) gauge theories.

Contribution

It constructs a non-local gauge-invariant order parameter for global symmetry breaking and numerically maps the transition lines in SU(2) and SU(3) gauge-Higgs theories.

Findings

Identification of a global symmetry-breaking transition in gauge-Higgs theories.

Existence of a transition between two confinement types: color neutrality and separation-of-charge confinement.

The symmetry-breaking transition likely coincides with the transition between these confinement regimes.

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.