Coulomb Energy, Remnant Symmetry, and the Phases of Non-Abelian Gauge Theories

TL;DR

This paper links the confining behavior of the Coulomb gauge gluon propagator to a remnant gauge symmetry, revealing a transition that distinguishes confined and Higgs phases in non-Abelian gauge theories.

Contribution

It introduces an order parameter for remnant gauge symmetry and demonstrates its behavior across different phases using numerical simulations.

Findings

Coulomb potential grows linearly in both confined and deconfined phases.

Remnant symmetry remains unbroken in the deconfined phase, contrary to expectations.

A remnant symmetry-breaking transition separates Higgs and confinement regions.

Abstract

We show that the confining property of the one-gluon propagator, in Coulomb gauge, is linked to the unbroken realization of a remnant gauge symmetry which exists in this gauge. An order parameter for the remnant gauge symmetry is introduced, and its behavior is investigated in a variety of models via numerical simulations. We find that the color-Coulomb potential, associated with the gluon propagator, grows linearly with distance both in the confined and - surprisingly - in the high-temperature deconfined phase of pure Yang-Mills theory. We also find a remnant symmetry-breaking transition in SU(2) gauge-Higgs theory which completely isolates the Higgs from the (pseudo)confinement region of the phase diagram. This transition exists despite the absence, pointed out long ago by Fradkin and Shenker, of a genuine thermodynamic phase transition separating the two regions.