303 research outputs found
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
Anderson localization through Polyakov loops: lattice evidence and Random matrix model
We investigate low-lying fermion modes in SU(2) gauge theory at temperatures
above the phase transition. Both staggered and overlap spectra reveal
transitions from chaotic (random matrix) to integrable (Poissonian) behavior
accompanied by an increasing localization of the eigenmodes. We show that the
latter are trapped by local Polyakov loop fluctuations. Islands of such "wrong"
Polyakov loops can therefore be viewed as defects leading to Anderson
localization in gauge theories. We find strong similarities in the spatial
profile of these localized staggered and overlap eigenmodes. We discuss
possible interpretations of this finding and present a sparse random matrix
model that reproduces these features.Comment: 11 pages, 23 plots in 11 figures; some comments and references added,
some axis labels corrected; journal versio
Linking confinement to spectral properties of the Dirac operator
We represent Polyakov loops and their correlators as spectral sums of
eigenvalues and eigenmodes of the lattice Dirac operator. The deconfinement
transition of pure gauge theory is characterized as a change in the response of
moments of eigenvalues to varying the boundary conditions of the Dirac
operator. We argue that the potential between static quarks is linked to
spatial correlations of Dirac eigenvectors.Comment: References and a comment added. To appear in PR
Quantitative comparison of filtering methods in lattice QCD
We systematically compare filtering methods used to extract topological
excitations (like instantons, calorons, monopoles and vortices) from lattice
gauge configurations, namely APE-smearing and spectral decompositions based on
lattice Dirac and Laplace operators. Each of these techniques introduces
ambiguities, which can invalidate the interpretation of the results. We show,
however, that all these methods, when handled with care, reveal very similar
topological structures. Hence, these common structures are free of ambiguities
and faithfully represent infrared degrees of freedom in the QCD vacuum. As an
application we discuss an interesting power-law for the clusters of filtered
topological charge.Comment: 6 pages, 18 plots in 5 figures; final version as published in EPJ A;
section 4 was adde
Cautionary remarks on the moduli space metric for multi-dyon simulations
We perform a detailed numerical investigation of the approximate moduli space
metric proposed by Diakonov and Petrov [arXiv:0704.3181] for a confining model
of dyons. Our findings strongly indicate that only for a small number of dyons
at sufficiently low density this metric is positive definite - and, therefore,
a valid moduli space metric - throughout a considerable part of configuration
space. This poses strong limitations on results obtained by an unrestricted
integration over collective coordinates in this model. It also indicates that
strong correlations between collective coordinates will be essential for the
physical content of a dyon model, which could be exhibited by a suitable
simulation algorithm.Comment: 20 pages, 6 figure
Deconfinement phase transition and the quark condensate
We study the dual quark condensate as a signal for the
confinement-deconfinement phase transition of QCD. This order parameter for
center symmetry has been defined recently by Bilgici et al. within the
framework of lattice QCD. In this work we determine the ordinary and the dual
quark condensate with functional methods using a formulation of the
Dyson-Schwinger equations for the quark propagator on a torus. The temperature
dependence of these condensates serves to investigate the interplay between the
chiral and deconfinement transitions of quenched QCD.Comment: 4 pages, 3 figures, v2: minor changes, typos corrected, version
accepted by PR
Probing for Instanton Quarks with epsilon-Cooling
We use epsilon-cooling, adjusting at will the order a^2 corrections to the
lattice action, to study the parameter space of instantons in the background of
non-trivial holonomy and to determine the presence and nature of constituents
with fractional topological charge at finite and zero temperature for SU(2). As
an additional tool, zero temperature configurations were generated from those
at finite temperature with well-separated constituents. This is achieved by
"adiabatically" adjusting the anisotropic coupling used to implement finite
temperature on a symmetric lattice. The action and topological charge density,
as well as the Polyakov loop and chiral zero-modes are used to analyse these
configurations. We also show how cooling histories themselves can reveal the
presence of constituents with fractional topological charge. We comment on the
interpretation of recent fermion zero-mode studies for thermalized ensembles at
small temperatures.Comment: 26 pages, 14 figures in 33 part
Local CP-violation and electric charge separation by magnetic fields from lattice QCD
We study local CP-violation on the lattice by measuring the local correlation
between the topological charge density and the electric dipole moment of
quarks, induced by a constant external magnetic field. This correlator is found
to increase linearly with the external field, with the coefficient of
proportionality depending only weakly on temperature. Results are obtained on
lattices with various spacings, and are extrapolated to the continuum limit
after the renormalization of the observables is carried out. This
renormalization utilizes the gradient flow for the quark and gluon fields. Our
findings suggest that the strength of local CP-violation in QCD with physical
quark masses is about an order of magnitude smaller than a model prediction
based on nearly massless quarks in domains of constant gluon backgrounds with
topological charge. We also show numerical evidence that the observed local
CP-violation correlates with spatially extended electric dipole structures in
the QCD vacuum.Comment: 19 pages, 7 figures. Additional lattice results about the induced
electric dipole structure, extended model description, specified terminology.
Version published in JHE
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