One-dimensional classical adjoint SU(2) Coulomb Gas

The equation of state of a one-dimensional classical nonrelativistic Coulomb gas of particles in the adjoint representation of SU(2) is given. The problem is solved both with and without sources in the fundamental representation at either end of the system. The gas exhibits confining properties at low densities and temperatures and deconfinement in the limit of high densities and temperatures. However, there is no phase transition to a regime where the string tension vanishes identically; true deconfinement only happens for infinite densities and temperatures. In the low density, low temperature limit, a new type of collective behavior is observed.Comment: 6 pages, 1 postscript figur

On the spectrum of QCD(1+1) with large numbers of flavours N_F and colours N_C near N_F/N_C = 0

QCD(1+1) in the limit of a large number of flavours N_F and a large number of colours N_C is examined in the small N_F/N_C regime. Using perturbation theory in N_F/N_C, stringent results for the leading behaviour of the spectrum departing from N_F/N_C = 0 are obtained. These results provide benchmarks in the light of which previous truncated treatments of QCD(1+1) at large N_F and N_C are critically reconsidered.Comment: 6 revtex page

Center Vortex Model for the Infrared Sector of SU(3) Yang-Mills Theory - Vortex Free Energy

The vortex free energy is studied in the random vortex world-surface model of the infrared sector of SU(3) Yang-Mills theory. The free energy of a center vortex extending into two spatial directions, which is introduced into Yang-Mills configurations when acting with the 't Hooft loop operator, is verified to furnish an order parameter for the deconfinement phase transition. It is shown to exhibit a weak discontinuity at the critical temperature, corresponding to the weak first order character of the transition.Comment: 13 pages, 2 figures containing 3 eps file

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

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

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