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 $\cal H$ 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