Markus Feurstein

Chaotic behavior of confining lattice Gauge field configurations

We analyze the leading Lyapunov exponents of SU(2) Yang-Mills field configurations on the lattice which are initialized by quantum Monte-Carlo simulations. We find that configurations in the strong coupling phase at finite temperature are substantially more chaotic than in deconfinement.

Visualization of topological objects in QCD

Abstract Recently evidence appeared that instantons and monopoles have a certain local correlation in four-dimensional pure SU (2) and SU (3) gauge theory. We visualize several specific gauge field configurations and show directly that there is an enhanced probability for finding maximally projected abelian monopole loops in the vicinity of instantons. This feature is independent of the topological charge definition used.

Visualization of topological structure and chiral condensate

Abstract We perform a mutual analysis of the topological and chiral vacuum structure of four-dimensional QCD on the lattice at finite temperature. We demonstrate that at the places where instantons are present, amplified production of quark condensate takes place. It turns out for full QCD that the clusters of nontrivial chiral condensate have a size of about 0.4 fm corresponding to the instanton sizes in the same configurations.

Visualization of chiral condensate at finite temperature on the lattice

Abstract We perform an analysis of the topological and chiral vacuum structure of four-dimensional QCD on the lattice at finite temperature. From correlation functions we show the existence of local correlations between the topological charge density and the quark condensate on gauge average. We comment on sizes of clusters of nontrivial chiral condensate and of instantons in full QCD. By analysis of individual gauge configurations, we demonstrate that at the places in Euclidian space-time, where instantons are present, amplified production of quark condensate occurs.

Topology without cooling: instantons and monopoles near to deconfinement☆

Abstract In an attempt to describe the change of topological structure of pure SU (2) gauge theory near deconfinement a renormalization group inspired method is tested. Instead of cooling, blocking and subsequent inverse blocking is applied to Monte Carlo configurations to capture topological features at a well-defined scale. We check that this procedure largely conserves long range physics like string tension. UV fluctuations and lattice artefacts are removed which otherwise spoil topological charge density and abelian monopole currents. We report the behaviour of topological susceptibility and monopole current densities across the deconfinement transition and relate the two faces of topology to each other. First results of a cluster analysis are described.

Topological and Chiral Structure in Lattice QCD at Finite Temperature

We perform an analysis of the topological and chiral vacuum structure of four-dimensional QCD on the lattice at finite temperature. It is demonstrated that at the places where instantons are present, amplified production of monopole currents and quark condensate takes place. We observe such nontrivial correlation functions also in the deconfinement phase and for single gauge field configurations. Values of the topological susceptibility across the temperature phase transition are reported.

Visualization of topological objects in the deconfinement phase of pure QCD

Abstract In the last years it turned out that instantons and monopoles have a certain local correlation in four-dimensional QCD. It was demonstrated by several groups independently and by different methods that at the locations of instantons also monopoles in the maximal abelian projection can be found with enhanced probability. Further we observed such nontrivial correlation functions in the deconfinement phase. We continue our visualization project to analyze several specific gauge-field configurations.

Correlation functions between topological objects — field theoretic versus geometric definitions

Abstract We analyze topological objects in pure gluonic SU (2) lattice gauge theory and compute correlation functions between instantons and monopoles. Concerning the instantons we use geometric and field theoretic definitions of the topological charge. On a 123 × 4 lattice it turns out that topological quantities have a non-trivial local correlation. The auto-correlation functions of the topological charge depend on cooling for both definitions. We fit the correlation functions to exponentials and obtain screening masses.

Instantons, monopoles and chiral symmetry breaking*

We analyze the interplay of topological objects in four dimensional QCD. The distributions of color magnetic monopoles obtained in the maximum abelian gauge are computed around instantons in both pure and full QCD. We find an enhanced probability of encountering monopoles inside the core of an instanton. We show this by means of local correlation functions of the topological variables. For specific gauge field configurations we visualize the situation graphically. Motivated by the fact that a fermion in the field of a static monopole has an energy zero mode we investigate how monopole loops and instantons are locally correlated with the chiral condensate. The observed correlations suggest that monopoles are involved in the mechanism of breaking of chiral symmetry.

Instanton-monopole correlations in lattice QCD

We analyze the interplay of topological objects in four dimensional QCD. The distributions of color magnetic monopoles obtained in the maximum abelian gauge are computed around instantons in four-dimensional full QCD. We find an enhanced probability of encountering monopoles inside the core of an instanton. Moreover we present evidence that nontrivial values of the chiral condensate are predominantly found at the locations of instantons and monopoles.