Infrared behavior and infinite-volume limit of gluon and ghost propagators in Yang-Mills theories

TL;DR

This study uses lattice simulations and rigorous bounds to analyze the infrared behavior of gluon and ghost propagators in Yang-Mills theories, providing insights into confinement and the infinite-volume limit.

Contribution

It introduces a method using susceptibility and eigenmodes to rigorously bound propagators, improving extrapolation to infinite volume in lattice studies.

Findings

Gluon propagator remains finite at zero momentum.

Ghost propagator enhancement in the infrared is unlikely.

Volume dependence of bounds confirms finite gluon propagator.

Abstract

Lattice studies of the infrared behavior of gluon and ghost propagators are a key probe of confinement scenarios in Yang-Mills theories. However, finite-volume effects become an important issue as the infrared limit is approached. By considering general quantities -- namely an associated susceptibility in the gluon case and properties of the lowest-lying eigenmode of the Faddeev-Popov matrix in the ghost case -- one can derive rigorous upper and lower bounds for the propagators. The bounds allow a better control over the extrapolation of lattice results to the infinite-volume limit. In the case of the gluon propagator, an intuitive statistical argument suggests a precise volume dependence for the bounds. This dependence is nicely confirmed by the lattice data, leading to a finite gluon propagator at zero momentum. At the same time, an enhancement of the ghost propagator in the infrared limit seems unlikely. Our analysis is applied to the case of Landau gauge and SU(2) gauge group, using the largest lattice sizes to date.