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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.

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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, 9 Apr 2024) in Chapter “Thermal Gluon Average”, Section “Infrared Gauge Fixing”, Subsection “Lattice Results”