On the gauge-algebra dependence of Landau-gauge Yang-Mills propagators

TL;DR

This study uses lattice gauge theory to examine whether Landau-gauge Yang-Mills propagators depend on the gauge algebra, finding only quantitative differences and no qualitative changes across various gauge groups and dimensions.

Contribution

The paper provides the first detailed lattice investigation of gauge-algebra dependence of Landau-gauge Yang-Mills propagators across multiple groups and dimensions, confirming theoretical predictions.

Findings

No qualitative dependence on gauge group found.

Non-perturbative effects persist at large N.

Quantitative differences are thoroughly analyzed.

Abstract

Yang-Mills theory can be formulated for any semi-simple Lie algebra, and thus any semi-simple Lie group. In principle, the dynamics could be different for each one. However, functional studies predict that the propagators in Landau gauge depend only quantitatively on the gauge algebra. In particular, genuine non-perturbative effects should be present even in the large N-limit for su(N) gauge algebras. Lattice gauge theory is used to investigate this in detail. The propagators are determined for the gauge groups SU(2), SU(3), SU(4), SU(5), SU(6) and G2, in two and three dimensions. In accordance with the prediction no qualitative dependence on the gauge group is found. In particular, no diminishing of non-perturbative contributions is found for N becoming large in the SU(N) case. Quantitative effects are found, and analyzed in detail.