Towards a unified viewpoint of Gribov--Zwanziger and Serreau--Tissier gauge fixing

TL;DR

The paper addresses the infrared Gribov problem by unifying two leading continuum approaches—ST copy averaging and RGZ horizon restriction—into a single, local, BRST-invariant gauge fixing. By combining the ST replica localization with RGZ horizon localization through the $A^h$ formulation, it constructs an interpolating action whose renormalizability is secured by algebraic renormalization, ensuring a consistent treatment of both sectors. IR dynamics are governed by coupled gap equations that fix horizon and condensate scales while the replica sector yields a radiatively generated gluon mass; an infrared matching ties the ST mass parameter to RGZ mass combinations, producing a gluon propagator that interpolates between ST-like and RGZ decoupling forms. The framework enables controlled studies of how infrared YM correlators depend on the balance between copy averaging and horizon suppression and suggests lattice tests with tunable copy weighting. This algebraic, BRST-consistent unification thus provides a practical bridge between two IR descriptions of Yang–Mills and a platform for quantitative comparisons with lattice and functional-method results.

Abstract

We investigate a unified Landau--gauge fixing that continuously interpolates between the viewpoints of the Serreau--Tissier (ST) copy-averaged formulation and the (Refined) Gribov--Zwanziger (RGZ) restriction to the first Gribov region. By combining the ST weight with a GZ-type horizon term and localizing both through the replica trick and the BRST-invariant $A_μ^h$ formulation, we obtain a single, local, BRST-invariant, power-counting renormalizable action. Algebraic renormalization shows that all counterterms are reabsorbed by a common set of field and parameter renormalizations, therefore the unification is algebraic rather than merely additive. The replica sector yields a radiatively generated gluon screening mass, while the RGZ parameters are fixed by the horizon and condensate gap equations; we also give infrared matching conditions that link both descriptions at small momentum. We present a compact BRST-superspace rewriting of the RGZ block and a simple hybrid superspace that hosts the ST replicas and RGZ side by side; these add no dynamics and organize the Ward-identity analysis. The resulting gluon propagator interpolates among the massive Faddeev--Popov--ST and the RGZ decoupling forms. This framework offers a controlled way to study how infrared Yang--Mills correlators depend on the balance between copy averaging and horizon suppression, and it suggests practical lattice tests through tunable copy weighting.