Center vortex properties in the Laplace-center gauge of SU(2) Yang–Mills theory

Abstract

Resorting to the the Laplace center gauge (LCG) and to the Maximal-center gauge (MCG), respectively, confining vortices are defined by center projection in either case. Vortex properties are investigated in the continuum limit of SU (2) lattice gauge theory. The vortex (area) density and the density of vortex crossing points are investigated. In the case of MCG, both densities are physical quantities in the continuum limit. By contrast, in the LCG the piercing as well as the crossing points lie dense in the continuum limit. In both cases, an approximate treatment by means of a weakly interacting vortex gas is not appropriate.

Topological susceptibility of Yang-Mills center projection vortices

“…In the latter, the center projection vortex density and its binary correlations measured in [32] scale properly under the renormalization group, such as to extrapolate to a finite physical result in the continuum limit, albeit with strong correlations in the ultraviolet, as discussed above. By contrast, it has recently been noted that in the Laplacian center gauge, the vortex density does not scale to a finite continuum limit, but appears to extrapolate to an infinite continuum density [30]. In a sense, the Laplacian center gauge may suffer from its own efficiency.…”

“…In terms of the underlying degrees of freedom, this presumably means that, in addition to the infrared structure of the theory, Laplacian center gauge fixing attempts to also partially represent ultraviolet perturbative gluons by vortices. This may be the reason for the unphysical renormalization group behavior observed for the density of Laplacian center gauge vortices [30].…”

The confinement problem in lattice gauge theory

“…Langfeld et al [76] have employed a combination of the LC and DMC gauges, first fixing to a unique configuration using the Laplacian center gauge, and subsequently relaxing to a nearby local maximum of the direct maximal center gauge. This amounts to selecting a particular Gribov copy of the DMC gauge, and is similar to the next center gauge we shall discuss.…”

Remarks on the Gribov problem in the direct maximal center gauge

“…The implication is that the measure of SA copies must be negligible compared to the measure of OR copies, at least at large volume. Both the volume and copy-number dependence of the projected Creutz ratio χ cp (5,5) at β = 2.5 are illustrated in Fig. 4, taken from ref.…”

“…Before proceeding, we should note that the Gribov problem can be avoided altogether by using the Laplacian center gauge [4]. On the other hand, the Laplacian version does have certain unattractive features, notably the lack of scaling of the Pvortex density [5] and the lack of "precocious linearity" [6]. While these features of Laplacian center gauge are by no means fatal, we think it worthwhile to further explore the Gribov copy issue in the older proposal of maximal center gauge.…”