GribovZwanziger

The Gribov-Zwanziger framework is a formulation of non-Abelian gauge theories that addresses the Gribov ambiguity arising in gauge fixing. It aims to make the gauge-fixed functional integral more faithful to the underlying gauge structure by restricting the integration to a region where gauge copies are absent or suppressed, notably the first Gribov region where the Faddeev-Popov operator is positive.

The Gribov problem arises because standard gauge-fixing procedures leave residual gauge copies. Gribov proposed restricting the configuration space to avoid infinitesimal copies, defining the boundary by the vanishing of the FP operator. This restriction introduces a nonlocal term, often referred to as the horizon function, into the gauge-fixed action.

Zwanziger demonstrated how to implement this restriction in a local, renormalizable action by introducing auxiliary bosonic and fermionic fields. The resulting Gribov-Zwanziger action contains a parameter, the Gribov gamma, determined self-consistently by a gap (horizon) equation. In the absence of this restriction, the action reduces to the conventional gauge-fixed theory.

Infrared consequences of the Gribov-Zwanziger framework include suppression of the gluon propagator at low momenta and a modified, often enhanced, ghost propagator. The framework also implies a soft breaking of BRST symmetry in the infrared and introduces a nonperturbative mass scale through the Gribov parameter.

Extensions such as the refined Gribov-Zwanziger approach include condensates of auxiliary fields and gauge fields, producing a decoupling-type gluon propagator that aligns more closely with lattice QCD results. The Gribov-Zwanziger scenario remains a prominent approach to understanding confinement and infrared dynamics in non-Abelian gauge theories.