The Higgs phase as a spin glass phase in D=5 dimensional SU(2) gauge Higgs theory

TL;DR

This paper investigates the phase structure of a five-dimensional SU(2) gauge-Higgs theory, testing recent ideas about symmetry breaking distinguishing Higgs, confinement, and massless phases, and finds evidence supporting these distinctions.

Contribution

It provides the first non-abelian gauge theory analysis in five dimensions confirming the role of a global center symmetry in phase distinctions.

Findings

The Higgs phase is characterized by spontaneous breaking of a global center subgroup.

Transition lines separate the massless from Higgs and confinement from Higgs phases.

No transition line is observed between the massless and confinement phases.

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.