FWF Project "Confinement and topological Configurations"

Project number: P20330

Project duration: 1st of January 2008-31st of December 2008

Project members: Christof Gattringer, Axel Maas

The confinement of color charges in Yang-Mills theory is a challenging and unresolved problem since many decades. Recently, two aspects have received much attention. The linear rise of the static quark-anti-quark potential (and also chiral symmetry breaking) has been attributed to topological configurations like vortices and monopoles. On the other hand, confinement in the gauge-sector seems eventually to be understandable in the framework of the Gribov-Zwanziger and the Kugo-Ojima scenario, and is manifest in the Green's functions of the theory.

First attempts to unify these two very different aspects of confinement have only been made in the last few years, and it seems that indeed both aspects are linked. This manifests itself in the changes of the Green's functions when manipulating the topological contents.

Based on this, the aims in this project are threefold: First, it aims to study the systematic dependence of topological configurations on various gauges and gauge-groups, to identify persistent topological structures. Second, the link between both aspects of confinement seems currently to be the spectrum of the Faddeev-Popov operator. Its dependence on the gauge and gauge-groups is also to be systematically analyzed. Finally, the dependence of various Green's functions, especially those describing gluons, on the topological contributions should be analyzed by systematically manipulating the latter.

The method of choice for these investigations will be lattice gauge theory, and part of the project will be devoted to developing the adequate numerical algorithms to achieve the scientific goals of this project.

The combined information from these three objectives will provide further insight into the link between the various confinement scenarios, and also into the properties of topological configurations. As the latter are also linked to hadronic physics via chiral symmetry, this will in the future also potentially contribute to a better first-principle understanding of the properties of hadrons and thus, ultimately, experiments.

Publications:

• J. Danzer et al., Chiral symmetry and spectral properties of the Dirac operator in G2 Yang-Mills Theory(Submitted to JHEP; ; October 2008)
• C. S. Fischer et al., On the infrared behavior of Landau gauge Yang-Mills theory(Submitted to PRD; arxiv:0810.1987 [hep-ph]; October 2008)
• J. Danzer et al., " Winding expansion techniques for lattice QCD with chemical potential" (arxiv:0809.2736 [hep-lat]; September 2009)
• A. Maas, More on Gribov copies and propagators in Landau-gauge Yang-Mills theory(Submitted to PRD; arxiv:0808.3047 [hep-lat]; August 2008)
• A. Cucchieri et al., Linear covariant gauges on the lattice (Accepted by CPC; arxiv:0806.3124 [hep-lat]; June 2008)
• A. Cucchieri et al., Three-point vertices in Landau-gauge Yang-Mills theory (Phys. Rev. D 77, 094510 (2008); arxiv:0803.1798 [hep-lat]; March 2008)
• E. Bilgici, "Static quark-antiquark potential and Dirac eigenvector correlators" (JHEP 0805:030,2008; arxiv:0803.1127 [hep-lat]; March 2008)
• E. Bilgici, "Dual quark condensate and dressed Polyakov loops" (Phys.Rev.D77:094007,2008; arxiv:0801.4051 [hep-lat]; January 2008)