Using a standard cooling method for SU(3) lattice gauge fields constant Abelian magnetic field configurations are extracted after dyon-antidyon constituents forming metastable Q=0 configurations have annihilated. These so-called Dirac sheets, standar
d and non-standard ones, corresponding to the two U(1) subgroups of the SU(3) group, have been found to be stable if emerging from the confined phase, close to the deconfinement phase transition, with sufficiently nontrivial Polyakov loop values. On a finite lattice we find a nice agreement of the numerical observations with the analytic predictions concerning the stability of Dirac sheets depending on the value of the Polyakov loop.
We study the Landau gauge gluon and ghost propagators of SU(3) gauge theory, employing the logarithmic definition for the lattice gluon fields and implementing the corresponding form of the Faddeev-Popov matrix. This is necessary in order to consiste
ntly compare lattice data for the bare propagators with that of higher-loop numerical stochastic perturbation theory (NSPT). In this paper we provide such a comparison, and introduce what is needed for an efficient lattice study. When comparing our data for the logarithmic definition to that of the standard lattice Landau gauge we clearly see the propagators to be multiplicatively related. The data of the associated ghost-gluon coupling matches up almost completely. For the explored lattice spacings and sizes discretization artifacts, finite-size and Gribov-copy effects are small. At weak coupling and large momentum, the bare propagators and the ghost-gluon coupling are seen to be approached by those of higher-order NSPT.
Overlap fermions preserve a remnant of chiral symmetry on the lattice. They are a powerful tool to investigate the topological structure of the vacuum of Yang-Mills theory and full QCD. Recent results concerning the localization of topological charge
and the localization and local chirality of the overlap eigenmodes are reported. The charge distribution is radically different, if a spectral cut-off for the Dirac eigenmodes is applied. The density q(x) is changing from the scale-a charge density (with full lattice resolution) to the ultraviolet filtered charge density. The scale-a density, computed on the Linux cluster of LRZ, has a singular, sign-coherent global structure of co-dimension 1 first described by the Kentucky group. We stress, however, the cluster properties of the UV filtered topological density resembling the instanton picture. The spectral cut-off can be mapped to a bosonic smearing procedure. The UV filtered field strength reveals a high degree of (anti)selfduality at hot spots of the action. The fermionic eigenmodes show a high degree of local chirality. The lowest modes are seen to be localized in low-dimensional space-time regions.
Lattice results for the gluon propagator in SU(2) pure gauge theory obtained on large lattices are presented. Simulated annealing is used throughout to fix the Landau gauge. We concentrate on checks for Gribov copy effects and for scaling properties.
Our findings are similar to the ones in the SU(3) case, supporting the decoupling-type infrared behaviour of the gluon propagator.
We present one- and two-loop results for the ghost propagator in Landau gauge calculated in Numerical Stochastic Perturbation Theory (NSPT). The one-loop results are compared with available standard Lattice Perturbation Theory in the infinite-volume
limit. We discuss in detail how to perform the different necessary limits in the NSPT approach and discuss a recipe to treat logarithmic terms by introducing ``finite-lattice logs. We find agreement with the one-loop result from standard Lattice Perturbation Theory and estimate, from the non-logarithmic part of the ghost propagator in two-loop order, the unknown constant contribution to the ghost self-energy in the RI-MOM scheme in Landau gauge. That constant vanishes within our numerical accuracy.
We study the infrared behavior of the effective Coulomb potential in lattice SU(3) Yang-Mills theory in the Coulomb gauge. We use lattices up to a size of 48^4 and three values of the inverse coupling, beta=5.8, 6.0 and 6.2. While finite-volume effec
ts are hardly visible in the effective Coulomb potential, scaling violations and a strong dependence on the choice of Gribov copy are observed. We obtain bounds for the Coulomb string tension that are in agreement with Zwanzigers inequality relating the Coulomb string tension to the Wilson string tension.
For the gluon propagator of pure SU(2) lattice gauge theory in the Landau gauge we investigate the effect of Gribov copies and finite-volume effects. Concerning gauge fixing, we enlarge the accessible gauge orbits by adding non-periodic Z(2) gauge tr
ansformations and systematically employ the simulated annealing algorithm. Strategies to keep all Z(2) sectors under control within reasonable CPU time are discussed. We demonstrate that the finite-volume effects in the infrared regime become ameliorated. Reaching a physical volume of about (6.5 fm)^4, we find that the propagator, calculated with the indicated improvements, becomes flat in the region of smallest momenta. First signs in 4d of a final decrease towards vanishing momentum are discussed.
We present selected recent results of the QCDSF collaboration on the localization and dimensionality of low overlap eigenmodes and of the topological density in the quenched SU(3) vacuum. We discuss the correlations between the topological structure
revealed by overlap fermions without filtering and the confining monopole and P-vortex structure obtained in the Indirect Maximal Center Gauge.
