Gauge Invariant Properties of Abelian Monopoles

Using a renormalization group motivated smoothing technique, we investigate the large scale structure of lattice configurations at finite temperature, concentrating on Abelian monopoles identified in the maximally Abelian, the Laplacian Abelian, and the Polyakov gauge. Monopoles are mostly found in regions of large action and topological charge, rather independent of the gauge chosen to detect them. Gauge invariant properties around Abelian monopoles, the local non-Abelian action and topological density, are studied. We show that the local averages of these densities along the monopole trajectories are clearly above the background, which supports the existence of monopoles as physical objects. Characteristic changes of the vacuum structure at the deconfinement transition can be attributed to the corresponding Abelian monopoles, to an extent that depends on the gauge chosen for Abelian projection. All three Abelian projections reproduce the full SU (2) string tension within 10 % which is preserved by smoothing.