269 research outputs found
Laplacian modes probing gauge fields
We show that low-lying eigenmodes of the Laplace operator are suitable to
represent properties of the underlying SU(2) lattice configurations. We study
this for the case of finite temperature background fields, yet in the
confinement phase. For calorons as classical solutions put on the lattice, the
lowest mode localizes one of the constituent monopoles by a maximum and the
other one by a minimum, respectively. We introduce adjustable phase boundary
conditions in the time direction, under which the role of the monopoles in the
mode localization is interchanged. Similar hopping phenomena are observed for
thermalized configurations. We also investigate periodic and antiperiodic modes
of the adjoint Laplacian for comparison.
In the second part we introduce a new Fourier-like low-pass filter method. It
provides link variables by truncating a sum involving the Laplacian eigenmodes.
The filter not only reproduces classical structures, but also preserves the
confining potential for thermalized ensembles. We give a first characterization
of the structures emerging from this procedure.Comment: 43 pages, 26 figure
Calorons, Nahm's equations on S^1 and bundles over P^1xP^1
The moduli space of solutions to Nahm's equations of rank (k,k+j) on the
circle, and hence, of SU(2) calorons of charge (k,j), is shown to be equivalent
to the moduli of holomorphic rank 2 bundles on P^1xP^1 trivialized at infinity
with c_2=k and equipped with a flag of degree j along P^1x{0}. An explicit
matrix description of these spaces is given by a monad constructio
Writhe of center vortices and topological charge -- an explicit example
The manner in which continuum center vortices generate topological charge
density is elucidated using an explicit example. The example vortex
world-surface contains one lone self-intersection point, which contributes a
quantum 1/2 to the topological charge. On the other hand, the surface in
question is orientable and thus must carry global topological charge zero due
to general arguments. Therefore, there must be another contribution, coming
from vortex writhe. The latter is known for the lattice analogue of the example
vortex considered, where it is quite intuitive. For the vortex in the
continuum, including the limit of an infinitely thin vortex, a careful analysis
is performed and it is shown how the contribution to the topological charge
induced by writhe is distributed over the vortex surface.Comment: 33 latex pages, 10 figures incorporating 14 ps files. Furthermore,
the time evolution of the vortex line discussed in this work can be viewed as
a gif movie, available for download by following the PostScript link below --
watch for the cute feature at the self-intersection poin
Thermodynamic properties of QCD in external magnetic fields
We consider the effect of strong external electromagnetic fields on
thermodynamic observables in QCD, through lattice simulations with 1+1+1
flavors of staggered quarks at physical quark masses. Continuum extrapolated
results are presented for the light quark condensates and for their tensor
polarizations, as functions of the temperature and the magnetic field. We find
the light condensates to undergo inverse magnetic catalysis in the transition
region, in a manner that the transition temperature decreases with growing
magnetic field. We also compare the results to other approaches and lattice
simulations. Furthermore, we relate the tensor polarization to the spin part of
the magnetic susceptibility of the QCD vacuum, and show that this contribution
is diamagnetic.Comment: 13 pages, 9 figures, talks presented by FB and GE at Xth Quark
Confinement and the Hadron Spectrum, 8-12 October 2012, TUM Campus Garching,
Munich, German
Ein Modell fĂĽr verantwortungsvolles Handeln in der IT-Organisation
In der Betriebswirtschaft ist verantwortungsvolles Handeln, repräsentiert durch Konzepte wie Corporate Social Responsibility (CSR), Corporate Citizenship (CC) oder Nachhaltigkeit/Sustainability, eine in Forschung und Praxis breit diskutierte Thematik. Eine umfassende Übertragung der Problematik auf das IT-Management hat jenseits von isolierten Einzelthemen wie „Green IT“ etc. jedoch noch nicht stattgefunden. In diesem Beitrag wird deshalb ein Modell vorgestellt, welches auf der einen Seite einen ganzheitlichen Rahmen für verantwortungsvolles Handeln in der IT-Organisation eröffnet, und auf der anderen Seite Stellschrauben für die aktive, verantwortungsvolle Beeinflussung des Wettbewerbsumfelds aufzeigt. Konkretisiert wird das aufgezeigte Modell anhand verschiedener Maßnahmenfelder zur Umsetzung verantwortungsvollen Handelns
Magnetic susceptibility of QCD at zero and at finite temperature from the lattice
The response of the QCD vacuum to a constant external (electro)magnetic field is studied through the tensor polarization of the chiral condensate and the magnetic susceptibility at zero and at finite temperature. We determine these quantities using lattice configurations generated with the tree-level Symanzik improved gauge action and N-f 1 + 1 + 1 flavors of stout smeared staggered quarks with physical masses. We carry out the renormalization of the observables under study and perform the continuum limit both at T > 0 and at T = 0, using different lattice spacings. Finite size effects are studied by using various spatial lattice volumes. The magnetic susceptibilities chi(f) reveal a spin-diamagnetic behavior; we obtain at zero temperature chi(u) = -(2.08 +/- 0.08) GeV-2, chi(d) = -(2.02 +/- 0.09) GeV-2 and chi(s) = -(3.4 +/- 1.4) GeV-2 for the up, down and strange quarks, respectively, in the (MS) over bar scheme at a renormalization scale of 2 GeV. We also find the polarization to change smoothly with the temperature in the confinement phase and then to drastically reduce around the transition region
Species Doublers as Super Multiplets in Lattice Supersymmetry: Exact Supersymmetry with Interactions for D=1 N=2
We propose a new lattice superfield formalism in momentum representation
which accommodates species doublers of the lattice fermions and their bosonic
counterparts as super multiplets. We explicitly show that one dimensional N=2
model with interactions has exact Lie algebraic supersymmetry on the lattice
for all super charges. In coordinate representation the finite difference
operator is made to satisfy Leibnitz rule by introducing a non local product,
the ``star'' product, and the exact lattice supersymmetry is realized. The
standard momentum conservation is replaced on the lattice by the conservation
of the sine of the momentum, which plays a crucial role in the formulation.
Half lattice spacing structure is essential for the one dimensional model and
the lattice supersymmetry transformation can be identified as a half lattice
spacing translation combined with alternating sign structure. Invariance under
finite translations and locality in the continuum limit are explicitly
investigated and shown to be recovered. Supersymmetric Ward identities are
shown to be satisfied at one loop level. Lie algebraic lattice supersymmetry
algebra of this model suggests a close connection with Hopf algebraic exactness
of the link approach formulation of lattice supersymmetry.Comment: 34 pages, 2 figure
Ghost Condensates and Dynamical Breaking of SL(2,R) in Yang-Mills in the Maximal Abelian Gauge
Ghost condensates of dimension two in SU(N) Yang-Mills theory quantized in
the Maximal Abelian Gauge are discussed. These condensates turn out to be
related to the dynamical breaking of the SL(2,R) symmetry present in this gaugeComment: 16 pages, LaTeX2e, final version to appear in J. Phys.
Center Vortex Model for the Infrared Sector of SU(3) Yang-Mills Theory - Confinement and Deconfinement
The center vortex model for the infrared sector of Yang-Mills theory,
previously studied for the SU(2) gauge group, is extended to SU(3). This model
is based on the assumption that vortex world-surfaces can be viewed as random
surfaces in Euclidean space-time. The confining properties are investigated,
with a particular emphasis on the finite-temperature deconfining phase
transition. The model predicts a very weak first order transition, in agreement
with SU(3) lattice Yang-Mills theory, and also reproduces a consistent behavior
of the spatial string tension in the deconfined phase. The geometrical
structure of the center vortices is studied, including vortex branchings, which
are a new property of the SU(3) case.Comment: 22 pages, 12 figures (30 eps-files), uses LaTeX package "psfrag
Numerical properties of staggered quarks with a taste-dependent mass term
The numerical properties of staggered Dirac operators with a taste-dependent
mass term proposed by Adams [1,2] and by Hoelbling [3] are compared with those
of ordinary staggered and Wilson Dirac operators. In the free limit and on
(quenched) interacting configurations, we consider their topological
properties, their spectrum, and the resulting pion mass. Although we also
consider the spectral structure, topological properties, locality, and
computational cost of an overlap operator with a staggered kernel, we call
attention to the possibility of using the Adams and Hoelbling operators without
the overlap construction. In particular, the Hoelbling operator could be used
to simulate two degenerate flavors without additive mass renormalization, and
thus without fine-tuning in the chiral limit.Comment: 14 pages, 9 figures. V2: published version; important note added
regarding Hoelbling fermions, otherwise minor change
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