Landau Gauge QCD: Functional Methods versus Lattice Simulations

TL;DR

This paper discusses the differences between continuum and lattice approaches to Landau gauge QCD, proposing a reformulation to enable direct comparison and improve non-perturbative understanding of Green's functions.

Contribution

It introduces a new lattice reformulation of Landau gauge to align lattice simulations with continuum non-perturbative methods in QCD.

Findings

Identifies discrepancies between lattice and continuum results.

Proposes a reformulation to unify approaches.

Aims to enhance non-perturbative analysis of Green's functions.

Abstract

The infrared behaviour of QCD Green's functions in Landau gauge has been focus of intense study. Different non-perturbative approaches lead to a prediction in line with the conditions for confinement in local quantum field theory as spelled out in the Kugo-Ojima criterion. Detailed comparisons with lattice studies have revealed small but significant differences, however. But aren't we comparing apples with oranges when contrasting lattice Landau gauge simulations with these continuum results? The answer is yes, and we need to change that. We therefore propose a reformulation of Landau gauge on the lattice which will allow us to perform gauge-fixed Monte-Carlo simulations matching the continuum methods of local field theory which will thereby be elevated to a non-perturbative level at the same time.