Dr Michael Teper

Abstract:

We extend our previous study of magnetic monopole currents in the maximally Abelian gauge to larger lattices at small lattice spacings (204 at β=2.5 and 324 at β=2.5115). We confirm that at these weak couplings there continues to be one monopole cluster that is very much longer than the rest and that the string tension, K, is entirely due to it. The remaining clusters are compact objects whose population as a function of radius follows a power law that deviates from the scale invariant form, but much too weakly to suggest a link with the analytically calculable size distribution of small instantons. We also search for traces of Z(2) vortices in the Abelian projected fields, either as closed loops of "magnetic" flux or through appropriate correlations among the monopoles. We find, by direct calculation, that there is no confining condensate of such flux loops. We also find, through the calculation of doubly charged Wilson loops within the monopole fields, that there is no suppression of the q=2 effective string tension out to distances of at least r≃1.6/√K, suggesting that if there are any vortices they are not encoded in the monopole fields. ©1999 The American Physical Society.

Abstract:

We calculate the spectral density of the Dirac operator over an ensemble of configurations composed of overlapping instantons and anti-instantons. We find evidence that the spectral density diverges in the limit λ → 0. This indicates the breaking of chiral symmetry and also provides evidence that quenched QCD may be pathological in nature.

Abstract:

We calculate the mass spectra and string tensions of SU(2), SU(3), SU(4) and SU(5) gauge theories in 2+1 dimensions. We do so by simulating the corresponding lattice theories and then extrapolating dimensionless mass ratios to the continuum limit. We find that such mass ratios are, to a first approximation, independent of the number of colors, Nc, and that the remaining dependence can be accurately reproduced by a simple O(1/Nc2) correction. This provides us with a prediction of these mass ratios for all SU(Nc) theories in 2+1 dimensions and demonstrates that these theories are already "close" to Nc=∞ for Nc≥2. We find that the theory retains a non-zero confining string tension as Nc→∞ and that the dimensionful coupling g2 is proportional to 1/Nc at large Nc, when expressed in units of the dynamical length scale of the theory. During the course of these calculations we study in detail the effects of including over-relaxation in the Monte Carlo calculation, of using a mean-field improved coupling to extrapolate to the continuum limit, and the use of space-time asymmetric lattice actions to resolve heavy glueball correlators. ©1998 The American Physical Society.