Abelian dominance and the dual Meissner effect in local unitary gauges in SU(2) gluodynamics

Abstract

Performing highly precise Monte-Carlo simulations of SU(2) gluodynamics, we observe for the first time Abelian dominance in the confining part of the static potential in local unitary gauges such as the F12 gauge. We also study the flux-tube profile between the quark and antiquark in these local unitary gauges and find a clear signal of the dual Meissner effect. The Abelian electric field is found to be squeezed into a flux tube by the monopole supercurrent. This feature is the same as that observed in the non-local maximally Abelian gauge. These results suggest that the Abelian confinement scenario is gauge independent. Observing the important role of space-like monopoles in the Polyakov gauge also indicates that the monopoles defined on the lattice do not necessarily correspond to those proposed by 't Hooft in the context of Abelian projection.PACS numbers: 12.38. Aw,14.80.Hv,12.38.Gc Quark confinement phenomenon remains an important unsolved problem in quantum chromodynamics (QCD) [1]. One of the most intriguing conjecture for its mechanism is that the QCD vacuum behaves as a dual superconductor due to magnetic monopole condensation [2, 3], i.e., the color flux between a quark and an antiquark is squeezed into a stringlike tube as the Abrikosov vortex [4,5] through the dual Meissner effect, which yields a linear-confining potential. Although it is not straightforward to identify the corresponding monopoles in QCD in contrast to SUSY QCD [6] or the Georgi-Glashow model [7,8] with scalar fields, it is possible to reduce SU(3) QCD into an Abelian [U(1)] 2 theory with magnetic monopoles by a partial gauge fixing, also referred to as the Abelian projection [9], and to accommodate the above dual superconductor scenario [10].However, there are infinite ways of the partial gaugefixing. Numerically, an Abelian projection with non-local gauges such as the maximally Abelian (MA) gauge [11,12,13] has been found to support the Abelian confinement scenario beautifully [14,15,16,17]. On the other hand, the Abelian confinement mechanism has not been observed clearly so far for years in other general gauges in particular, in local unitary gauges [18,19,20]. This is very unsatisfactory, since the quark confinement mechanism should not depend on a special gauge choice [21].It is the purpose of this letter to show for the first time that the Abelian confinement mechanism is observed numerically also in local unitary gauges with the method of highly precise numerical simulations. For numerical simplicity we adopt SU(2) group instead of SU(3), but the essential feature of non-Abelian gauge theory should be the same. As local unitary gauges, we adopt simplest candidates, namely the F12, the F123 and the spatial Polyakov loop (SPL) gauges as well as the original Polyakov (PL) gauge. Applying the multi-level noise reduction method invented by Lüscher and Weisz [22], we investigate the Abelian static potential with high accuracy and find a clear signal of Abelian dominance in its confining part in all local unitary gauges considere...

Gauge independence of Abelian confinement mechansim in SU(2) gluodynamics

“…Numerically, an Abelian projection in non-local gauges such as the maximally Abelian (MA) gauge [7,8] has been found to support the Abelian confinement scenario beautifully [9,10]. Very recently, the present authors have shown that the Abelian dominance and the dual Meissner effect are observed clearly also in local unitary gauges such as F12 and Polyakov (PL) gauges [11]. These results strongly suggest that the Abelian confinement mechanism is gauge-independent.…”

Superconductivity in Restricted Chromo-Dynamics (RCD) in SU(2) and SU(3) Gauge Theories

“…This idea of Abelian dominance has recently been verified by gauge fixing and Abelian projection [35] and also by constructing semilocal models in Extended Abelian Higgs model (EAH-model) [36,37]. The same idea has been used, more recently, in connection with the dual Meissner effect in local unitary gauges in SU(2) gluo-dynamics [38] and also with confining ensemble of dyons [39] and dual superconductivity in Yang-Mills theories [40].…”

Superconductivity in Supersymmetric Theory in Restricted Chromodynamics

“…The similar result has also been obtained more recently in a dual superconductivity model [14] which places the Y -M vacuum close to the border between Type-I and Type-II superconductors and marginally on the Type-II side. The same idea of Abelian dominance has been used more recently in connection with the dual Meissner effect in local unitary gauges in SU(2) gluodynamic [49] and also with confining ensemble of dyons [50] and dual superconductivity in Yang-Mills theories [14].…”