No abstract

It has been well established that the removal of center vortices from SU(2) lattice configurations results in the loss of confinement. The running coupling constant, gluon form factor, and ghost form factor are studied in the Landau gauge for the full and the vortex removed theory. In the latter case, a strong suppression of the running coupling constant and the gluon form factor at low momenta is observed, and the IR singularity of the ghost form factor disappears. Hence, the removal of the vortices generates a theory for which Zwanziger's horizon condition for confinement is no longer satisfied.

We study the interplay between Dirac eigenmodes and center vortices in SU(2) lattice gauge theory. In particular we focus on vortex-removed configurations and compare them to an ensemble of configurations with random changes of the link variables. We show that removing the vortices destroys all zero modes and the near zero modes are no longer coupled to topological structures. The Dirac spectrum for vortex-removed configurations in many respects resembles a free spectrum thus leading to a vanishing chiral condensate. Configurations with random changes leave the topological features of the Dirac eigensystem intact. We finally show that smooth center vortex configurations give rise to zero modes and topological near zero modes.

In order to observe the confinement of quarks and gluons in Yang-Mills theory, two conditions must necessarily be obeyed [1]: (i) there must be a long range order of certain un-physical degrees of freedom (violation of the cluster decomposition ); (ii) there must be a mass gap for physical excitations. Using Landau gauge where the gauge configurations are restricted to the first Gribov regime, it was firstly speculated by Gribov [2] that the divergence of the ghost propagator at zero momentum transfer signals confinement. Over the years, Zwanziger has put forward that the configurations which are relevant for confinement are close to the Gribov horizon [3]. A formal relation between confinement and the IR properties of confinement was advocated by Kugo and Ojima [4]: their approach is based on the assumption that a unique definition of the BRST charge operator exists. This assumption, however, is invalidated by the presence of Gribov copies.In my talk, I will explore the relation between the IR properties of Green functions and confinement using SU(2) lattice gauge theory.Recent investigations of the Dyson-Schwinger equations [5,6] have revealed that the ghost-propagator G(p 2 ) and the gluon-propagator D(p

The high-temperature phase of SU (2) Yang-Mills theory is addressed by means of dimensional reduction with a special emphasis on the properties of center vortices. For this purpose, the vortex vacuum which arises from center projection is studied in pure 3-dimensional Yang-Mills theory as well as in the 3-dimensional adjoint Higgs model which describes the high temperature phase of the 4-dimensional SU (2) gauge theory. We find center-dominance within the numerical accuracy of 10%. a supported in part by Graduiertenkolleg Hadronen und Kerne b supported in part by grant DFG Re 856/4-1