Abstract
We propose that the Higgs phase of a gauge Higgs theory is the phase of spontaneously broken custodial symmetry, and present a new gauge invariant order parameter for custodial symmetry breaking which is very closely analogous to the Edwards-Anderson order parameter for spin glasses. Custodial symmetry is a global symmetry acting on the Higgs field alone, and we show here that the spin glass transition in gauge Higgs theories, from a QCD-like phase to a Higgs phase of broken custodial symmetry, coincides with the transition between two distinct types of confinement. These are color confinement in the Higgs phase, and a stronger version of confinement, which we have termed "separation-of-charge" confinement, in the QCD-like phase.
Highlights
In a gauge Higgs theory, with the scalar field in the fundamental representation of the gauge group, there is no thermodynamic transition which entirely separates the phase diagram into a confining and a Higgs phase [1,2]
There is a confining region which is qualitatively much like QCD, in the sense that there are metastable color electric flux tubes which break by pair creation, and, as a consequence, linear Regge trajectories whose resonances correspond to such metastable states
In previous work [3] we have suggested that the Higgs and confining regions are distinguished by different varieties of confinement, namely color (C) confinement in the Higgs region and a stronger type of confinement, which we call “separation of charge” (Sc) confinement, in the QCDlike region, and we have shown that there must be a sharp transition between these types of confinement [4]
Summary
In a gauge Higgs theory, with the scalar field in the fundamental representation of the gauge group, there is no thermodynamic transition which entirely separates the phase diagram into a confining and a Higgs phase [1,2]. There is a Higgs region, in which all forces mediated by bosons are Yukawa in character, as in the weak interaction sector of the Standard Model, and there is no flux tube formation at any length scale The physics of these two regions, like the physics of QCD and the weak interactions, is qualitatively so different that one may ask whether the distinction may be formulated precisely, despite the absence of a thermodynamic separation. The purpose of this article is to introduce a new criterion for custodial symmetry breaking which is very closely analogous to the Edwards-Anderson order parameter for spin glass transitions [9], and to show that custodial symmetry breaking according to the new criterion coincides physically with the transition from Sc to C confinement This implies that the Higgs regime of a gauge Higgs theory can be regarded as a spin glass phase
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