7,068 research outputs found
Center vortex model for the infrared sector of Yang-Mills theory
A model for the infrared sector of SU(2) Yang-Mills theory, based on magnetic
vortices represented by (closed) random surfaces, is presented. The model
quantitatively describes both confinement (including the finite-temperature
transition to a deconfined phase) and the topological susceptibility of the
Yang-Mills ensemble. A first (quenched) study of the spectrum of the Dirac
operator furthermore yields a behavior for the chiral condensate which is
compatible with results obtained in lattice gauge theory.Comment: Lattice2001(confinement) proceedings, 3 pages, 3 ps figure
Center vortex model for the infrared sector of SU(3) Yang-Mills theory: Topological susceptibility
The topological susceptibility of the SU(3) random vortex world-surface
ensemble, an effective model of infrared Yang-Mills dynamics, is investigated.
The model is implemented by composing vortex world-surfaces of elementary
squares on a hypercubic lattice, supplemented by an appropriate specification
of vortex color structure on the world-surfaces. Topological charge is
generated in this picture by writhe and self-intersection of the vortex
world-surfaces. Systematic uncertainties in the evaluation of the topological
charge, engendered by the hypercubic construction, are discussed. Results for
the topological susceptibility are reported as a function of temperature and
compared to corresponding measurements in SU(3) lattice Yang-Mills theory. In
the confined phase, the topological susceptibility of the random vortex
world-surface ensemble appears quantitatively consistent with Yang-Mills
theory. As the temperature is raised into the deconfined regime, the
topological susceptibility falls off rapidly, but significantly less so than in
SU(3) lattice Yang-Mills theory. Possible causes of this deviation, ranging
from artefacts of the hypercubic description to more physical sources, such as
the adopted vortex dynamics, are discussed.Comment: 30 pages, 6 figure
Center vortex model for the infrared sector of SU(4) Yang-Mills theory: String tensions and deconfinement transition
A random vortex world-surface model for the infrared sector of SU(4)
Yang-Mills theory is constructed, focusing on the confinement properties and
the behavior at the deconfinement phase transition. Although the corresponding
data from lattice Yang-Mills theory can be reproduced, the model requires a
more complex action and considerably more tuning than the SU(2) and SU(3) cases
studied previously. Its predictive capabilities are accordingly reduced. This
behavior has a definite physical origin, which is elucidated in detail in the
present work. As the number of colors is raised in Yang-Mills theory, the
corresponding infrared effective vortex description cannot indefinitely
continue to rely on dynamics determined purely by vortex world-surface
characteristics; additional color structures present on the vortices begin to
play a role. As evidenced by the modeling effort reported here, definite
signatures of this behavior appear in the case of four colors.Comment: 24 pages, 7 figures containing 8 ps file
Center vortex model for the infrared sector of SU(3) Yang-Mills theory -- baryonic potential
The baryonic potential in the framework of the SU(3) random vortex
world-surface model is evaluated for a variety of static color source
geometries. For comparison, carefully taking into consideration the string
tension anisotropy engendered by the hypercubic lattice description, also the
Delta and Y law predictions for the baryonic potential are given. Only the Y
law predictions are consistent with the baryonic potentials measured.Comment: 13 LaTeX pages, 2 figures (3 ps files). Replacement contains
additional reference
Neutron electric polarizability from unquenched lattice QCD using the background field approach
A calculational scheme for obtaining the electric polarizability of the
neutron in lattice QCD with dynamical quarks is developed, using the background
field approach. The scheme differs substantially from methods previously used
in the quenched approximation, the physical reason being that the QCD ensemble
is no longer independent of the external electromagnetic field in the dynamical
quark case. One is led to compute (certain integrals over) four-point
functions. Particular emphasis is also placed on the physical role of constant
external gauge fields on a finite lattice; the presence of these fields
complicates the extraction of polarizabilities, since it gives rise to an
additional shift of the neutron mass unrelated to polarizability effects. The
method is tested on a SU(3) flavor-symmetric ensemble furnished by the MILC
Collaboration, corresponding to a pion mass of m_pi = 759 MeV. Disconnected
diagrams are evaluated using stochastic estimation. A small negative electric
polarizability of alpha =(-2.0 +/- 0.9) 10^(-4) fm^3 is found for the neutron
at this rather large pion mass; this result does not seem implausible in view
of the qualitative behavior of alpha as a function of m_pi suggested by Chiral
Effective Theory.Comment: 36 pages, 11 figures. Note added concerning analytic continuation in
the external electric field; some notation made more precis
Energy Density of Vortices in the Schroedinger Picture
The one-loop energy density of an infinitely thin static magnetic vortex in
SU(2) Yang-Mills theory is evaluated using the Schroedinger picture. Both the
gluonic fluctuations as well as the quarks in the vortex background are
included. The energy density of the magnetic vortex is discussed as a function
of the magnetic flux. The center vortices correspond to local minima in the
effective potential. These minima are degenerated with the perturbative vacuum
if the fermions are ignored. Inclusion of fermions lifts this degeneracy,
raising the vortex energy above the energy of the perturbative vacuum.Comment: 25 pages, 2 figure
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