New Abelian-like monopoles and the dual Meissner effect

TL;DR

This paper investigates Abelian-like monopoles in SU(N) QCD, demonstrating their continuum limit, gauge dependence, and role in the dual Meissner effect, supporting the idea of gauge-invariant monopole dominance in confinement.

Contribution

It introduces a new analysis of Abelian-like monopoles in SU(N) QCD, showing their continuum limit, gauge independence, and effectiveness in explaining the dual Meissner effect.

Findings

Monopole dominance improves with block-spin transformations.

Electric fields are squeezed by Abelian-like monopoles in various gauges.

SU(2) vacuum is near the border between type 1 and type 2 dual superconductors.

Abstract

Violation of non-Abelian Bianchi identity can be regarded as $N^2-1$ Abelian-like monopole currents in the continuum SU(N) QCD. Three Abelian-like monopoles, when defined in SU(2) gluodynamics on the lattice \`{a} la DeGrand-Toussaint, are shown to have the continuum limit with respect to the color-invariant monopole density and the effective monopole action. Since each Abelian-like monopole is not gauge invariant, we have introduced various partial gauge fixing for the purpose of reducing lattice artifact monopoles in the thermalized vacuum. Here we investigate Abelian and monopole dominances and the Abelian dual Meissner effects adopting the same gauges like the maximal center gauge (MCG) in comparison with the maximal Abelian gauge (MAG). Abelian and monopole contributions to the string tension in these gauges are observed to be a little smaller than the non-Abelian string tension. However, we find that the monopole dominance is improved well when use is made of the block-spin transformations with respect to Abelian-like monopoles. We find each electric field is squeezed by the corresponding colored Abelian-like monopole in such gauges and the Abelian dual Meissner effect is observed independently for each color. Moreover, we confirm the dual Amp\`{e}re's law in these new gauges as well as in MAG. The SU(2) vacuum is shown to be near the border between the type 1 and type 2 dual superconductors. The penetration length is almost equal for the four gauge fixings and the vacuum type in MCG is almost the same value as the previous results. These results are consistent with the previous results suggesting the continuum limit and the gauge-independence of Abelian monopoles.