Resolution of the Gribov copy problem

Establish a complete and rigorous resolution of the Gribov copy problem in Landau-gauge Yang–Mills theory, determining how to consistently treat gauge copies in the functional integral beyond the Faddeev–Popov action so that infrared properties can be derived from first principles.

Background

The lectures explain that lattice results contradict the infrared behavior predicted by the Faddeev–Popov action (scaling vs. decoupling), indicating the need for a replacement or extension in the infrared. They attribute the core difficulty to the Gribov copy problem: the existence of multiple gauge-equivalent configurations satisfying the same gauge-fixing condition.

A definitive theoretical resolution of the Gribov copy problem would clarify how to construct a gauge-fixed continuum framework consistent with infrared lattice data. In the absence of such a resolution, the lectures employ the Curci–Ferrari model as a phenomenological approach.

References

Of course, finding what this something else is is a complicated matter because it relates to the Gribov copy problem which remains an open problem to date.

— Aspects of confinement within non-Abelian gauge theories  (2404.06118 - Reinosa, 2024) in Chapter “Thermal Gluon Average”, Section “Infrared Gauge Fixing”, Subsection “Lattice Results”

It remains an open question if every gauge orbit still passes through \Omega in the presence of planar boundaries.

— Examples of Gribov copies in the presence of planar boundaries, and an emergent boundary gauge invariance in Yang-Mills theory  (2608.30447 - Dudal et al., 31 Aug 2026) in Section 3, subsection “Gribov copies and zero-modes with finite L_2-norm”

Note that this is an approximation we are making here, as after all there could also be a Gribov ambiguity for the dimensionally reduced 3D theory taking the full non-Abelian nature into account . We will leave this for future work but already briefly comment about it in our outlook.

— The Casimir effect in Gribov-Zwanziger theory  (2609.11448 - Dudal et al., 10 Sep 2026) in Footnote in Section 3, subsection “Effective boundary action”