Infrared saturation and phases of gauge theories with BRST symmetry

• Published in: The European physical journal. C, Particles and fields Vol. 74; no. 5; pp. 2881 - 20
• Main Authors: Mader, Valentin, Schaden, Martin, Zwanziger, Daniel, Alkofer, Reinhard
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2014; Springer Nature B.V
• Subjects: Astronomy; Astrophysics and Cosmology; Bosons; Coulomb friction; Elementary Particles; Gages; Gauges; Hadrons; Heavy Ions; Infrared; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Phases; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular - Theoretical Physics; Regular Article - Theoretical Physics; Saturation; String Theory; Symmetry
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-014-2881-8

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.