Lattice QCD Green's functions in maximally Abelian gauge: infrared Abelian dominance and the quark sector

Abstract

On lattice gauge field configurations with 2+1 dynamical quark flavors, we investigate the momentum space quark and gluon propagators in the combined maximally Abelian plus $U(1{)}_3\times U(1{)}_8$ Landau gauge. We extract the gluon fields from the lattice link variables and study the diagonal and off-diagonal gluon propagators. We find that the infrared region of the transverse diagonal gluon propagator is strongly enhanced compared to the off-diagonal propagator. The Dirac operator from the Asqtad action is inverted on the diagonal and off-diagonal gluon backgrounds separately. In agreement with the hypothesis of infrared Abelian dominance, we find that the off-diagonal gluon background hardly gives rise to any non-trivial quark dynamics while the quark propagator from the diagonal gluon background closely resembles its Landau gauge counterpart.

9 pages, 6 figures; revised v2: references added

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• Gribov no-pole condition, Zwanziger horizon function, Kugo-Ojima confinement criterion, boundary conditions, BRST breaking and all that
• Dielectric function of the QCD vacuum
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Cited by in corpus (3)

• More on the non-perturbative Gribov-Zwanziger quantization of linear covariant gauges
• A non-perturbative study of matter field propagators in Euclidean Yang-Mills theory in linear covariant, Curci-Ferrari and maximal Abelian gauges
• Study of the all orders multiplicative renormalizability of a local matter confining Gribov-Zwanziger action in the MAG