Dr Michael Teper

Abstract:

We show that the monopole currents which one obtains in the maximally Abelian gauge of SU(2) fall into two quite distinct classes (when the volume is large enough). In each field configuration there is precisely one cluster that permeates the whole lattice volume. It has a current density and a magnetic screening mass that scale and it produces the whole of the string tension. The remaining clusters have a number density that follows an approximate power law [Formula Presented] where [Formula Presented] is the length of the monopole world line in lattice units. These clusters are localized in space-time with radii which vary as [Formula Presented]. In terms of the radius [Formula Presented] these “lumps” have a scale-invariant distribution [Formula Presented]. Moreover they appear not to contribute at all to the string tension. The fact that they are scale invariant at small distances would seem to rule out an instanton origin. © 1998 The American Physical Society.

Abstract:

We present a study of the instanton size and spatial distributions in pure SU(3) gauge theory using under-relaxed cooling. We also investigate the low-lying eigenmodes of the (improved) Wilson-Dirac operator, in particular, the appearance of zero-modes and their space-time localisation with respect to instantons in the underlying gauge field.

Abstract:

We compare the mass spectra and string tensions of SU(2), SU(3) and SU(4) gauge theories in 2+1 dimensions. We find that the ratios of masses are, to a first approximation, independent of Nc and that the remaining dependence can be accurately reproduced by a simple O(1/N2c) 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 'close' to Nc = ∞ for Nc ≥ 2. We also find that, when expressed in units of the dynamical length scale of the theory, the dimensionful coupling g2 is proportional to 1/Nc at large Nc. We confirm that these theories are indeed confining in the limit Nc → ∞. We describe preliminary calculations in 3+1 dimensions which indicate that the same will be true there. © 1997 Elsevier Science B.V.