Infrared Saturation and Phases of Gauge Theories with BRST Symmetry

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.

19 pages; v2: abstract rewritten, a few comments and references added; v3: title changed, major revision of the Introduction and some further minor revisions; version agrees with the one to be published in Eur. Phys. J. C

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• Constraining the gauge-fixed Lagrangian in minimal Landau gauge
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• Poincare' Symmetry of the GZ-Model
• Lattice QCD Green's functions in maximally Abelian gauge: infrared Abelian dominance and the quark sector
• Center phase transition from matter propagators in (scalar) QCD
• Low momentum propagators at two loops in gluon mass model
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