3,916 research outputs found
Status of center dominance in various center gauges
We review arguments for center dominance in center gauges where vortex
locations are correctly identified. We introduce an appealing interpretation of
the maximal center gauge, discuss problems with Gribov copies, and a cure to
the problems through the direct Laplacian center gauge. We study correlations
between direct and indirect Laplacian center gauges.Comment: Presented by S. Olejnik at the NATO Advanced Research Workshop
"Confinement, Topology, and other Non-Perturbative Aspects of QCD", Jan.
21-27, 2002, Stara Lesna, Slovakia. 10 pages, 3 figures (8 EPS files), uses
crckapb.st
Malmquist Bias and the Distance to the Virgo Cluster
This paper investigates the impact of Malmquist bias on the distance to the
Virgo cluster determined by the H_0 Key Project using M100, and consequently on
the derived value of H_0. Malmquist bias is a volume-induced statistical effect
which causes the most probable distance to be different from the raw distance
measured. Consideration of the bias in the distance to the Virgo cluster raises
this distance and lowers the calculated value of H_0. Monte Carlo simulations
of the cluster have been run for several possible distributions of spirals
within the cluster and of clusters in the local universe. Simulations
consistent with known information regarding the cluster and the errors of
measurement result in a bias of about 6.5%-8.5%. This corresponds to an
unbiased distance of 17.2-17.4 Mpc and a value of H_0 in the range 80-82
km/s/Mpc.
The problem of determining the bias to Virgo illustrates several key points
regarding Malmquist bias. Essentially all conventional astronomical distance
measurements are subject to this bias. In addition, the bias accumulates when
an attempt is made to construct "distance ladders" from measurements which are
individually biased. As will be shown in the case of Virgo, the magnitude and
direction of the bias are sensitive to the spatial distribution of the parent
poputation from which the observed object is drawn - a distribution which is
often poorly known. This leads to uncertainty in the magnitude of the bias, and
adds to the importance of minimizing the number of steps in "distance ladders".Comment: 19 pages, 3 figures, Latex, To appear in Ap
Remarks on the Gribov Problem in Direct Maximal Center Gauge
We review the equivalence of maximal center gauge fixing to the problem of
finding the best fit, to a given lattice gauge field, by a thin vortex
configuration. This fit is necessarily worst at the location of P-plaquettes.
We then compare the fits achieved in Gribov copies generated by (i)
over-relaxation; (ii) over-relaxation after Landau gauge preconditioning; and
(iii) simulated annealing. Simulated annealing yields the best fit if all links
on the lattice are included, but the situation changes if we consider only the
lattice volume exterior to P-plaquettes. In this exterior region, the fit is
best for Gribov copies generated by over-relaxation, and worst for Gribov
copies generated after Landau gauge preconditioning. The two fitting criteria
(including or not including the P-plaquettes) yield string tensions differing
by -34% to +20% respectively, relative to the full string tension. Our usual
procedure (``quenched minimization'') seems to be a compromise between these
criteria, and yields string tensions at an intermediate value close to the full
string tension.Comment: 14 pages, 6 figure
Abelian representation for nonabelian Wilson loops and the Non - Abelian Stokes theorem on the lattice
We derive the Abelian - like expression for the lattice SU(N) Wilson loop in
arbitrary irreducible representation. The continuum Abelian representation of
the SU(N) Wilson loop (for the loop without selfintersections) that has been
obtained by Diakonov and Petrov appears to be a continuum limit of this
expression. We also obtain the lattice variant of a non - Abelian Stokes
theorem and present the explicit expression for the matrix used in the
Diakonov - Petrov approach.Comment: revtex, 10 pages, ITEP-LAT/2002-3
On the relevance of center vortices to QCD
In a numerical experiment, we remove center vortices from an ensemble of
lattice SU(2) gauge configurations. This removal adds short-range disorder.
Nevertheless, we observe long-range order in the modified ensemble: confinement
is lost and chiral symmetry is restored (together with trivial topology),
proving that center vortices are responsible for both phenomena. As for the
Abelian monopoles, they survive but their percolation properties are lost.Comment: 4 pages, 5 figures; discussion expanded, text compressed... to appear
in Phys. Rev. Let
Topological Susceptibility of Yang-Mills Center Projection Vortices
The topological susceptibility induced by center projection vortices
extracted from SU(2) lattice Yang-Mills configurations via the maximal center
gauge is measured. Two different smoothing procedures, designed to eliminate
spurious ultraviolet fluctuations of these vortices before evaluating the
topological charge, are explored. They result in consistent estimates of the
topological susceptibility carried by the physical thick vortices
characterizing the Yang-Mills vacuum in the vortex picture. This susceptibility
is comparable to the one obtained from the full lattice Yang-Mills
configurations. The topological properties of the SU(2) Yang-Mills vacuum can
thus be accounted for in terms of its vortex content.Comment: 12 revtex pages, 6 ps figures included using eps
Characterizing normal crossing hypersurfaces
The objective of this article is to give an effective algebraic
characterization of normal crossing hypersurfaces in complex manifolds. It is
shown that a hypersurface has normal crossings if and only if it is a free
divisor, has a radical Jacobian ideal and a smooth normalization. Using K.
Saito's theory of free divisors, also a characterization in terms of
logarithmic differential forms and vector fields is found and and finally
another one in terms of the logarithmic residue using recent results of M.
Granger and M. Schulze.Comment: v2: typos fixed, final version to appear in Math. Ann.; 24 pages, 2
figure
Vortex critical behavior at the de-confinement phase transition
The de-confinement phase transition in SU(2) Yang-Mills theory is revisited
in the vortex picture. Defining the world sheets of the confining vortices by
maximal center projection, the percolation properties of the vortex lines in
the hypercube consisting of the time axis and two spatial axis are studied.
Using the percolation cumulant, the temperature for the percolation transition
is seen to be in good agreement with the critical temperature of the thermal
transition. The finite size scaling function for the cumulant is obtained. The
critical index of the finite size scaling function is consistent with the index
of the 3D Ising model.Comment: 4 pages, 4 PS figures, using revtex4, paragraph and refs added, typo
correcte
Massless Thirring model in canonical quantization scheme
It is shown that the exact solvability of the massless Thirring model in the
canonical quantization scheme originates from the intrinsic linearizability of
its Heisenberg equations in the method of dynamical mappings. The corresponding
role of inequivalent representations of free massless Dirac field is
elucidated.Comment: 10 page
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