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

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

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

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

Large center vortices and confinement in 3D Z(2) gauge theory

We study the role of large clusters of center vortices in producing confinement in 3D Z(2) gauge theory. First, we modify each configuration of a Monte Carlo-generated ensemble in the confined phase by removing the largest cluster of center vortices, and show that the ensemble thus obtained does not confine. Conversely, we show that removing all of the small clusters of center vortices and leaving the largest one only, confinement is preserved, albeit with a string tension significantly smaller than the original one. Remarkably, also the string corrections due to the quantum fluctuations of the confining flux tube are preserved by this transformation.Comment: 8 pages,5 figure

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

Low temperature magnetization and the excitation spectrum of antiferromagnetic Heisenberg spin rings

Accurate results are obtained for the low temperature magnetization versus magnetic field of Heisenberg spin rings consisting of an even number N of intrinsic spins s = 1/2, 1, 3/2, 2, 5/2, 3, 7/2 with nearest-neighbor antiferromagnetic (AF) exchange by employing a numerically exact quantum Monte Carlo method. A straightforward analysis of this data, in particular the values of the level-crossing fields, provides accurate results for the lowest energy eigenvalue E(N,S,s) for each value of the total spin quantum number S. In particular, the results are substantially more accurate than those provided by the rotational band approximation. For s <= 5/2, data are presented for all even N <= 20, which are particularly relevant for experiments on finite magnetic rings. Furthermore, we find that for s > 1 the dependence of E(N,S,s) on s can be described by a scaling relation, and this relation is shown to hold well for ring sizes up to N = 80 for all intrinsic spins in the range 3/2 <= s <= 7/2. Considering ring sizes in the interval 8 <= N <= 50, we find that the energy gap between the ground state and the first excited state approaches zero proportional to 1/N^a, where a = 0.76 for s = 3/2 and a = 0.84 for s = 5/2. Finally, we demonstrate the usefulness of our present results for E(N,S,s) by examining the Fe12 ring-type magnetic molecule, leading to a new, more accurate estimate of the exchange constant for this system than has been obtained heretofore.Comment: Submitted to Physical Review B, 10 pages, 10 figure

Temporal dynamics and fitness consequences of coalition formation in male primates

Coalition formation is one of the most striking forms of cooperation found in animals. Yet, there is substantial variation between taxa regarding the mechanisms by which coalitions can result in fitness consequences. Here, we investigate the influence of coalitions on dominance rank trajectories and subsequently on reproductive success in wild male crested macaques (Macaca nigra) at Tangkoko Nature Reserve (Sulawesi, Indonesia). We observed 128 coalition events involving 28 males and tested how a variety of coalition properties and factors related to the social environment influenced future male rank. We further used genetic paternity analysis of 19 infants conceived during the study to assess male reproductive success. Our results show that males participating in coalitions achieved higher-than-expected future ranks, while coalition targets had lower-than-expected future ranks. Additionally, all-up coalitions had stronger effects on rank than all-down and bridging coalitions, and these were modulated by the relative strength of coalition partners versus targets. Finally, higher ranking males were more likely to sire infants than lower ranking males. These results provide important insights regarding the mechanisms underlying coalition formation and support the idea that one major path by which coalitions can affect fitness is through influencing male dominance trajectories

Vortex structures in pure SU(3) lattice gauge theory

The structures of confining vortices which underlie pure SU(3) Yang-Mills theory are studied by means of lattice gauge theory. Vortices and Z_3 monopoles are defined as dynamical degrees of freedom of the Z_3 gauge theory which emerges by center gauge fixing and by subsequent center projection. It is observed for the first time for the case of SU(3) that these degrees of freedom are sensible in the continuum limit: the planar vortex density and the monopole density properly scales with the lattice spacing. By contrast to earlier findings concerning the gauge group SU(2), the effective vortex theory only reproduces 62% of the full string tension. On the other hand, however, the removal of the vortices from the lattice configurations yields ensembles with vanishing string tension. SU(3) vortex matter which originates from Laplacian center gauge fixing is also discussed. Although these vortices recover the full string tension, they lack a direct interpretation as physical degrees of freedom in the continuum limit.Comment: 25 pages, 13 ps figures, improved presentation, results unchange