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Register a new userCalorons and monopoles from smeared SU(2) lattice fields at non-zero temperature
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Authors
E.-M. Ilgenfritz
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In equilibrium, at finite temperature below and above the deconfining phase transition, we have generated lattice SU(2) gauge fields and have exposed them to smearing in order to investigate the emerging clusters of topological charge. Analysing in addition the monopole clusters according to the maximally Abelian gauge, we have been able to characterize part of the topological clusters to correspond either to non-static calorons or static dyons in the context of Kraan-van Baal caloron solutions with non-trivial holonomy. We show that the relative abundance of these calorons and dyons is changing with temperature and offer an interpretation as dissociation of calorons into dyons with increasing temperature. The profile of the Polyakov loop inside the topological clusters and the (model-dependent) accumulated topological cluster charges support this interpretation. Above the deconfining phase transition light dyons (according to Kraan-van Baal caloron solutions with almost trivial holonomy) become the most abundant topological objects. They are presumably responsible for the magnetic confinement in the deconfined phase.
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By cooling of equilibrium lattice fields at finite temperature in SU(2) gauge theory it has been shown that topological objects (calorons) observed on the lattice in the confined phase possess a dyonic substructure which becomes visible under certain circumstances. Here we show that, with decreasing temperature of the equilibrium ensemble, the distribution in the caloron parameter space is modified such that the calorons appear non-dissociated into constituent dyons. Still the calorons have nontrivial holonomy which is demonstrated by the Polyakov line behaviour for these configurations. At vanishing temperature (on a symmetric lattice) topological lumps obtained by cooling possess rotational symmetry in 4D and a characteristic double peak structure of Polyakov lines (defined with respect to temporal and spatial directions) with non-trivial asymptotics.
We study SU(2) lattice gauge theory at $T>0$ in a finite box with fixed holonomy value at the spatial boundary. We search for (approximate) classical solutions of the lattice field equations and find in particular the dissociated calorons recently discussed by van Baal and collaborators.
We report on our search for Kraan-van Baal calorons in finite temperature SU(2) lattice ensembles. We also discuss recent progress made in developing a caloron-anticaloron gas model decribing confinement and deconfinement in the context of trivial and non-trivial holonomy.
We investigate SU(2) lattice gauge theory in four dimensions in the maximally abelian projection. Studying the effects on different lattice sizes we show that the deconfinement transition of the fields and the percolation transition of the monopole currents in the three space dimensions are precisely related. To arrive properly at this result the uses of a mathematically sound characterization of the occurring networks of monopole currents and of an appropriate method of gauge fixing turn out to be crucial. In addition we investigate detailed features of the monopole structure in time direction.
We investigate propagators in Lorentz (or Landau) gauge by Monte Carlo simulations. In order to be able to compare with perturbative calculations we use large $beta$ values. There the breaking of the Z(2) symmetry turns out to be important for all of the four lattice directions. Therefore we make sure that the analysis is performed in the correct state. We discus implications of the gauge fixing mechanism and point out the form of the weak-coupling behavior to be expected in the presence of zero-momentum modes. Our numerical result is that the gluon propagator in the weak-coupling limit is strongly affected by zero-momentum modes. This is corroborated in detail by our quantitative comparison with analytical calculations.
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