Particle theory

Abstract:

In the maximally Abelian gauge of SU(2), the clusters of monopole current are found to divide into two distinct classes. The largest cluster permeates the lattice, has a density that scales and produces the string tension. The remaining clusters possess an approximate 1/l3 number density distribution (1 is the cluster length), their radii vary as √1 and their total current density does not scale. Their contribution to the string tension is compatible with being exactly zero. Their number density can be thought of as arising from an underlying scale invariant distribution. This suggests that they are not related to instantons. We also observe that when we locally smoothen the SU(2) fields by cooling, the string tension due to monopoles becomes much smaller than the SU(2) string tension. This dramatic loss of Abelian/monopole dominance occurs even after just one cooling step.

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.