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

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.