Numerical studies of confinement in the lattice Landau gauge

TL;DR

This study numerically investigates confinement in lattice Landau gauge, examining Gribov copy effects and testing the Kugo-Ojima criterion and Gribov-Zwanziger theory predictions through various simulation methods.

Contribution

It provides a comparative analysis of different gauge simulation techniques and their impact on confinement-related parameters, confirming theoretical expectations about the horizon function.

Findings

Gribov copy effects on the Kugo-Ojima parameter are minimal.

Different simulation methods yield consistent results with scale differences.

The horizon function remains negative across all gauges tested.

Abstract

Critical conjectures on confinement in the Landau gauge is numerically tested in focus to Gribov copy effects. One of the subjects is of the Kugo-Ojima confinement criterion and the other is of various viewpoints in the Gribov-Zwanziger theory. We use the smearing gauge as a reference gauge free of Gribov copy, and performed three types of simulations, log U, U-linear and log U in the smearing gauge. It is found that Gribov copy effect on the Kugo-Ojima parameter is small. log U and U-linear simulations yield only global scale factor difference in gluon propagator and in ghost propagator, and about 10% difference in Kugo-Ojima parameter. The horizon function defined by Zwanziger is evaluated in three types of gauge field and compared. All data show the negative horizon function as expected.