Vortices, Confinement and Higgs fields

We review lattice evidence for the vortex mechanism of quark confinement and study the influence of charged matter fields on the vortex distribution.Comment: 10 pages, 6 eps figures, talk presented by M.F. at the 5th International Conference "Quark Confinement and the Hadron Spectrum", Gargnano, Italy, September 10-14, 200

Vortices in the SU(2)-Higgs model -- Vortices and the covariant adjoint Laplacian

Vortices in the SU(2)--Higgs model: The presence of a fundamental Higgs in the SU(N)-Higgs model yields color screening at some finite distance. Whereas the transition to the Higgs "phase" is accompanied by a suppression of projected center vortices, there is nearly no influence of color screening on the vortex properties in the confined "phase". Hence the behavior of the Wilson loop can be described in both phases within the vortex picture of confinement. Vortices and the covariant adjoint Laplacian: Laplacian center gauge is a method to localize center vortices in SU(N) gauge theory. We show that the eigenvectors of the covariant adjoint Laplacian identify vortices for a special class of gauge field configurations. However, for Monte Carlo generated configurations, modified approaches are required.Comment: 3 pages, 4 figures; Lattice2001(confinement

Susceptibility of Monte-Carlo Generated Projected Vortices

We determine the topological susceptibility from center projected vortices and demonstrate that the topological properties of the SU(2) Yang-Mills vacuum can be extracted from the vortex content. We eliminate spurious ultraviolet fluctuations by two different smoothing procedures. The extracted susceptibility is comparable to that obtained from full field configurations.Comment: 3 pages, 4 figures; Lattice2001(confinement

Center Dominance in SU(2) Gauge-Higgs Theory

We study the SU(2) gauge-Higgs system in D=4 dimensions, and analyze the influence of the fundamental-representation Higgs field on the vortex content of the gauge field. It is shown that center projected Polyakov lines, at low temperature, are finite in the infinite volume limit, which means that the center vortex distribution is consistent with color screening. In addition we confirm and further investigate the presence of a "Kertesz-line" in the strong-coupling region of the phase diagram, which we relate to the percolation properties of center vortices. It is shown that this Kertesz-line separates the gauge-Higgs phase diagram into two regions: a confinement-like region, in which center vortices percolate, and a Higgs region, in which they do not. The free energy of the gauge-Higgs system, however, is analytic across the Kertesz line.Comment: 7 pages, 10 figure

The vortex model in lattice quantum chromo dynamics

Als Quarkeinschluss wird die Erkenntnis bezeichnet, dass die fundamentalen Fermionen der Quantenchromodynamik (QCD) nicht als freie Teilchen, sondern stets als Bausteine zusammengesetzter Teilchen, nämlich der Hadronen, auftreten.Der Quarkeinschluss kann im Rahmen der Gitter-QCD, welche die kontinuierliche Raumzeit durch ein diskretes euklidisches Gitter ersetzt, durch nichtstörungstheoretische analytische Rechnungen wie auch durch numerische Simulation der QCD durch das Monte-Carlo-Verfahren gezeigt werden.Es existiert trotzdem noch immer kein unumstrittenes Modell für den Mechanismus des Quarkeinschlusses in der QCD.Durch die fortschreitende Rechentechnik ist es in den letzten Jahren möglich geworden, ein bereits in den Siebzigern entwickeltes Modell, das Vortexmodell, numerisch am Gitter zu überprüfen.Im Vortexmodell ist das Zentrum der Eichgruppe von entscheidender Bedeutung; in unseren Rechnungen verwenden wir hierfür zumeist nicht die SU(3) der QCD, sondern die einfachere Gruppe SU(2).Wir untersuchen inwieweit die Zentrumsfreiheitsgrade der Eichfeldkonfigurationen extrahiert werden können, und beleuchten die Vorteile und Mängel der verschiedenen Vortexdetektionsmethoden.Die Anregungen der Zentrumsfreiheitsgrade werden als P-Vortices bezeichnet; wir finden dass diese als komplizierte, nichtorientierbare Zufallsflächen, die das ganze Gitter durchziehen, dargestellt werden können.Diese und andere Vortexeigenschaften stehen in guter Übereinstimmung mit den Anforderungen für die Erklärung des Quarkeinschlusses.Diese gute Übereinstimmung finden wir auch in Systemen bei endlicher Temperatur, solche in der Phase des Quark-Gluon-Plasmas, und auch in Systemen mit dynamischen Materiefeldern, in denen der Mechanismus des Quarkeinschlusses mehr oder weniger abgeändert ist.Schlussendlich wird das Vortexmodell auch auf andere Infraroteigenschaften der QCD, nämlich auf die Brechung der chiralen Symmetrie und auf die topologischen Eigenschaften, angewandt.Konkret zeigen wir, wie die topologische Suszeptibilität aus den extrahierten P-Vortices berechnet werden kann.Auf diese Weise liefert das Vortexmodell ein vereinheitlichtes Bild für den infraroten, niederenergetischen Sektor der QCD, das sowohl den Quarkeinschluss als auch die chiralen und topologischen Eigenschaften beschreibt.Being part of the standard model of particle physics, quantum chromo dynamics (QCD) is generally believed to be the correct theory of the strong interactions.A particular feature of QCD is that its fundamental fermions, the quarks, cannot be observed as free particles, but are always confined in composite particles, the hadrons, such as the protons and neutrons.Due to the large value of the strong coupling constant g, perturbation theory, which can treat successfully QCD at high energies, cannot be applied to the low energy problem of confinement.One method to investigate low energy QCD is to regularise the theory reducing the continuous space-time to a discrete Euclidean lattice.This opens the way both for analytical calculations and for numerical simulations of QCD on computers via Monte Carlo methods.But although confinement could be persuasively shown on the lattice, there exists still no indisputable model explaining how confinement exactly emerges from QCD.In the last years there has arisen a new interest for the vortex model of confinement.This model has already been suggested in the seventies, but only since the late nineties the improving computer technology enabled numerical tests of the vortex model on the lattice.The vortex model claims that the center of the gauge group is crucial for confinement; in this work we investigate how, for the gauge group SU(2), the center degrees of freedom can be extracted from gauge field configurations.The excitations of the extracted d.o.f. are dubbed as P-vortices and can be represented by two-dimensional surfaces on the four-dimensional lattice; they are thought to indicate objects present in configurations before the extraction step.These objects are called thick vortices, carry quantised magnetic center charges and are responsible for confinement according to the vortex model.In detailed numerical studies we show how using appropriate gauges one can successfully detect vortices, we highlight the shortcomings of various detection methods and investigate how to overcome these shortcomings.Next we look at the properties of the extracted P-vortex surfaces; we find that they are complicated, unorientable random surfaces percolating through the lattice.These and other P-vortex properties are in good agreement with the requirements to explain confinement.The connection between vortex properties and confinement is further extended to systems at finite temperature, in the phase of the quark-gluon plasma, and to systems with dynamical matter fields.For all these systems confinement is more or less changed, and this is properly reflected in the investigated vortex properties.Finally, the vortex model could be applied to other infrared features of QCD not immediately related to confinement, namely chiral symmetry breaking and the topological properties.In particular we show how the topological susceptibility present in QCD can be accurately calculated from the extracted P-vortex surfaces.This way the vortex model provides an unified picture for the infrared, low energy sector of QCD explaining both confinement and the chiral and topological features of the strong interaction.15