Infrared Saturation and Phases of Gauge Theories with BRST Symmetry

TL;DR

This paper analyzes the infrared behavior of gauge theories with BRST symmetry, showing how the saturation of the gauge boson propagator distinguishes between Coulomb, Higgs, and confining phases, with implications for confinement criteria.

Contribution

It introduces a phase classification based on the saturation of the gauge boson propagator's equation of motion in various gauges with BRST symmetry, extending confinement criteria.

Findings

Coulomb phase has a massless gauge boson.

Higgs phase saturation involves physical states.

Confining phase saturation is due to unphysical degrees of freedom.

Abstract

We investigate the infrared limit of the quantum equation of motion of the gauge boson propagator in various gauges and models with a BRST symmetry. We find that the saturation of this equation at low momenta distinguishes between the Coulomb, Higgs and confining phase of the gauge theory. The Coulomb phase is characterized by a massless gauge boson. Physical states contribute to the saturation of the transverse equation of motion of the gauge boson at low momenta in the Higgs phase, while the saturation is entirely due to unphysical degrees of freedom in the confining phase. This corollary to the Kugo-Ojima confinement criterion in linear covariant gauges also is sufficient for confinement in general covariant gauges with BRST- and anti-BRST symmetry, maximal Abelian gauges with an equivariant BRST symmetry, non-covariant Coulomb gauge and in the Gribov-Zwanziger theory.