On the infrared behavior of Green's functions in Yang-Mills theory

TL;DR

This paper uses lattice gauge theory to numerically investigate the infrared behavior of propagators and vertices in SU(2) Yang-Mills theory across different gauges, dimensions, and temperatures, supporting the Gribov-Zwanziger confinement scenario.

Contribution

It provides comprehensive numerical results for Green's functions in SU(2) Yang-Mills theory, including finite-volume effects, gauge dependence, and temperature effects, validating theoretical confinement models.

Findings

Results support the Gribov-Zwanziger confinement scenario.

Infrared behavior is consistent across gauges and dimensions.

Finite-temperature effects influence the propagators near the deconfinement transition.

Abstract

Non-perturbative properties of QCD, such as color confinement, are encoded in the infrared behavior of correlation functions, e.g. propagators and vertices. Various analytic predictions have been suggested for these quantities in various gauges. Here we numerically test these predictions using lattice gauge theory. In particular, we present results for the 2- and 3-point functions for SU(2) Landau-gauge Yang-Mills theory in three and in four dimensions. Special attention is paid to systematic finite-volume effects. The gluon and ghost propagators are also evaluated in the so-called interpolating gauge (between the Landau and the Coulomb gauge), in order to study their gauge-dependence. Finally, we consider these propagators in Landau gauge at finite temperature, with the aim of understanding the effect of the deconfinement phase transition on their infrared behavior. All our results are compatible with the so-called Gribov-Zwanziger confinement scenario.