Spontaneous breaking of residual gauge symmetries on the lattice

TL;DR

This paper investigates how residual gauge symmetries in lattice gauge theories can spontaneously break at weak coupling, revealing a phase transition that challenges assumptions about gauge equivalence.

Contribution

It demonstrates the spontaneous breaking of residual gauge symmetries on the lattice and links this to phase transitions observed in Monte-Carlo simulations.

Findings

Residual gauge symmetry breaks spontaneously at weak coupling.

Phase transition coincides with deconfinement transition.

Results observed in both Z2 and SU(2) gauge theories.

Abstract

Lattice gauge theories are considered with a partial axial gauge fixing along one direction only. This leaves a residual gauge symmetry that is still local in three directions but now global in one. It is found that this $N^{d-1}$ fold symmetry (on an $N^d$ lattice) breaks spontaneously at weak coupling with the gauge field elements on links averaged over 1-d chains along the gauge-fixing direction as order parameters. This phase transition is observed with Monte-Carlo simulations for both 3-d Z2 and 4-d SU(2) pure gauge theories and appears to be coincident with the deconfinement transition. This work calls into question the equivalence of different gauges in certain circumstances.