1,456 research outputs found
Topological objects in QCD
Topological excitations are prominent candidates for explaining
nonperturbative effects in QCD like confinement. In these lectures, I cover
both formal treatments and applications of topological objects. The typical
phenomena like BPS bounds, topology, the semiclassical approximation and chiral
fermions are introduced by virtue of kinks. Then I proceed in higher dimensions
with magnetic monopoles and instantons and special emphasis on calorons.
Analytical aspects are discussed and an overview over models based on these
objects as well as lattice results is given.Comment: 28 pages, 17 figures; Lectures given at 45th Internationale
Universitaetswochen fuer Theoretische Physik (International University School
of Theoretical Physics): Conceptual and Numerical Challenges in Femto- and
Peta-Scale Physics, Schladming, Styria, Austria, 24 Feb - 3 Mar 200
Filtered topological structure of the QCD vacuum: Effects of dynamical quarks
We systematically compare filtering methods used to extract topological
structures on SU(3) lattice configurations. We show that there is a strong
correlation of the topological charge densities obtained by APE and Stout
smearing. To get rid of artifacts of these methods, we analyse structures that
are also seen by Laplace filtering and indeed identify artifacts for strong
smearing. The topological charge density in this combined analysis is more
fragmented in the presence of dynamical quarks. A power law exponent that
characterises the distribution of filtered topological clusters turns out to be
not far off the values of an instanton gas model.Comment: 7 pages, 6 figures, final version to appear in PL
Pointlike Hopf defects in Abelian projections
We present a new kind of defect in Abelian Projections, stemming from
pointlike zeros of second order. The corresponding topological quantity is the
Hopf invariant pi_3(S^2) (rather than the winding number pi_2(S^2) for magnetic
monopoles). We give a visualisation of this quantity and discuss the simplest
non-trivial example, the Hopf map. Such defects occur in the Laplacian Abelian
gauge in a non-trivial instanton sector. For general Abelian projections we
show how an ensemble of Hopf defects accounts for the instanton number.Comment: talk given at the XVIII Autumn School `Topology of strongly
correlated systems', Lisbon, October 2000; to appear in the proceedings
(World Scientific); latex, 4 pages, 2 figure
On the zero of the fermion zero mode
We argue that the fermionic zero mode in non-trivial gauge field backgrounds
must have a zero. We demonstrate this explicitly for calorons where its
location is related to a constituent monopole. Furthermore a topological
reasoning for the existence of the zero is given which therefore will be
present for any non-trivial configuration. We propose the use of this property
in particular for lattice simulations in order to uncover the topological
content of a configuration.Comment: 6 pages, 3 figures in 5 part
Hopf defects as seeds for monopole loops
We investigate the relation between instantons and monopoles in the Laplacian
Abelian Gauge using analytical methods in the continuum. Our starting point is
the fact that the 't Hooft instanton with its high symmetry leads to a
pointlike defect with Hopf invariant one. In order to generalise this result we
partly break the symmetry by a local perturbation. We find that for generic
configurations near the 't Hooft instanton the defects become loops. The
analytical results show explicitly that these defects are magnetic monopoles
with unit charge. In addition, the monopoles are twisted to account for the
instanton number of the background.Comment: latex, 6 pages, 2 figures; v2: references added, emphasis modified,
conclusions unchange
Laplacian modes as a filter
We compute low-lying eigenmodes of the gauge covariant Laplace operator on
the lattice at finite temperature. For classical configurations we show how the
lowest mode localizes the monopole constituents inside calorons and that it
hops upon changing the boundary conditions. The latter effect we observe for
thermalized backgrounds, too, analogously to what is known for fermion zero
modes.
We propose a new filter for equilibrium configurations which provides link
variables as a truncated sum involving the Laplacian modes. This method not
only reproduces classical structures, but also preserves the confining
potential, even when only a few modes are used.Comment: talk presented by FB at the Workshop on Computational Hadron Physics,
Nikosia (Cyprus), Sept. 14-17, 2005; compared to hep-lat/0509020 and
hep-lat/0509087 we have added the following points: 1. the kinetic term
(square of the covariant derivative) as an analyzing observable, 2. the
correlation of filtered link variables to the original ones, 3. the filtered
string tension from modes with shifted ordinal number; 8 pages, 8 figures,
uses espcrc2.st
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