Nonperturbative QCD, gauge-fixing, Gribov copies, and the lattice

TL;DR

This paper discusses the challenges of gauge-fixing in nonperturbative QCD, comparing approaches like Gribov-copy free gauges and BRST invariance, and relates Dyson-Schwinger models to lattice results.

Contribution

It analyzes the implications of gauge-fixing choices in nonperturbative QCD and connects Dyson-Schwinger models with lattice calculations of Green's functions.

Findings

Gribov copies are negligible in perturbative regime

Lattice and Dyson-Schwinger approaches provide complementary insights

Different gauge-fixing methods impact nonperturbative QCD studies

Abstract

Perturbative QCD uses the Faddeev-Popov gauge-fixing procedure, which leads to ghosts and the local BRST invariance of the gauge-fixed perturbative QCD action. In the asymptotic regime, where perturbative QCD is relevant, Gribov copies can be neglected. In the nonperturbative regime, one must adopt either a nonlocal Gribov-copy free gauge (e.g., Laplacian gauge) or attempt to maintain local BRST invariance at the expense of admitting Gribov copies. These issues are explored. In addition, we discuss the relationship between recent Dyson-Schwinger based model calculations of the infrared behavior of QCD Green's functions and the lattice calculation of these quantities.