Landau gauge ghost and gluon propagators and the Faddeev-Popov operator spectrum

TL;DR

This paper presents a lattice study of Landau gauge ghost and gluon propagators in SU(3) gauge theory, examining the Faddeev-Popov spectrum, the ghost-gluon vertex, and the impact of Gribov copies, revealing insights into infrared behavior and spectral properties.

Contribution

It provides the first SU(3) lattice computation of the ghost-gluon vertex and analyzes the Faddeev-Popov operator spectrum in the context of Landau gauge.

Findings

Infrared gluon and ghost propagators show specific behavior at low momenta.

The ghost-gluon vertex remains nearly constant, indicating weak deviation.

The Faddeev-Popov spectrum reveals details about gauge fixing and Gribov copies.

Abstract

In this talk we report on a recent lattice investigation of the Landau gauge gluon and ghost propagators in pure SU(3) lattice gauge theory with a special emphasis on the Gribov copy problem. In the (infrared) region of momenta $q^2 \le 0.3 \mathrm{GeV}^2$ we find the corresponding MOM scheme running coupling $\alpha_s(q^2)$ to rise in $q$. We also report on a first SU(3) computation of the ghost-gluon vertex function showing that it deviates only weakly from being constant. In addition we study the spectrum of low-lying eigenvalues and eigenfunctions of the Faddeev-Popov operator as well as the spectral representation of the ghost propagator.