Reconsidering gauge-Higgs continuity

TL;DR

This paper demonstrates that in the 3-d Z(2) lattice gauge-Higgs theory, a residual symmetry breaks spontaneously in the Higgs phase and remains unbroken in the confinement phase, indicating a phase transition contrary to previous theorems.

Contribution

It reveals that the gauge-Higgs theory with an unfixed gauge exhibits a phase transition separating the Higgs and confinement phases, challenging earlier assumptions based on fully fixed gauges.

Findings

Residual Z(2) symmetry breaks in Higgs phase

No symmetry breaking in confinement phase

Contradicts Fradkin-Shenker theorem

Abstract

The 3-d Z(2) lattice gauge-Higgs theory is cast in a partial axial gauge leaving a residual Z(2) symmetry, global in two directions and local in one. It is shown both analytically and numerically that this symmetry breaks spontaneously in the Higgs phase and is unbroken in the confinement phase. Therefore they must be separated everywhere by a phase transition, in contradiction to a theorem by Fradkin and Shenker. It relied on a fully fixed unitary gauge, which prohibits this phase transition explicitly. Thus the unfixed gauge theory is not, in this case, equivalent to the unitary-gauge version.