Abelian Projections and Monopoles

Chernodub, M. N.; Polikarpov, M.I.

doi:10.1007/0-306-47056-x_14

Cited by 59 publications

(90 citation statements)

References 45 publications

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“…Due to a non-zero string tension the quark and the antiquark are confined by a linear potential. This mechanism has been confirmed by many numerical simulations of the lattice gluodynamics 3), 4) which show that the abelian monopoles in the Maximal Abelian projection are responsible for the confinement. The SU (2) string tension is well described by the contribution of the abelian monopole currents 5) ; these currents satisfy the London equation for a superconductor 6), 7) .…”

Section: §1 Introductionmentioning

confidence: 64%

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Monopoles in the Abelian Projection of Gluodynamics

Chernodub

Gubarev

Polikarpov

et al. 1998

Prog. Theor. Phys. Suppl.

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We discuss some properties of the abelian monopoles in compact U (1) gauge theory and in the SU (2) gluodynamics both on the lattice and in the continuum. §1. IntroductionAbelian monopoles play a key role in the dual superconductor mechanism of confinement 1) in non-abelian gauge theories. Abelian monopoles appear after the so called abelian projection 2) . According to the dual superconductor mechanism a condensation of abelian monopoles should give rise to the formation of an electric flux tube between the test quark and antiquark. Due to a non-zero string tension the quark and the antiquark are confined by a linear potential. This mechanism has been confirmed by many numerical simulations of the lattice gluodynamics 3), 4) which show that the abelian monopoles in the Maximal Abelian projection are responsible for the confinement. The SU (2) string tension is well described by the contribution of the abelian monopole currents 5) ; these currents satisfy the London equation for a superconductor 6), 7) . In Fig. 1, taken from Ref. 7) , the abelian monopole currents near the center of the flux tube formed by the quark-anti-quark pair are shown. It is seen that the monopoles wind around the center of the flux tube just as the Cooper pairs wind around the center of the Abrikosov string. In Fig. 2 taken from Ref. 8) we show the dependence of the value of the monopole condensate Φ inf c on β is shown. It is clearly seen that Φ inf c vanishes at the phase transition and it plays the role of the order parameters 8), 9) . In Ref. 10) the effective lagrangian for monopoles was reconstructed from numerical data for monopole currents for SU (2) gluodynamics in the Maximal Abelian gauge. It occurs that this lagrangian corresponds to the Abelian Higgs model, the monopole are condensed in the classical string tension of the Abrikosov-Nielsen-Olesen string describes well the quantum string tension of the SU (2) gluodynamics. It means that the description of the gluodynamics at large distances in terms of the monopole variables can be very useful.

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Section: §1 Introductionmentioning

confidence: 64%

“…Below we give a short review of the recently obtained results; for the elementary introduction to the subject see Ref. 4) . Since the abelian monopoles play a dominant role in the confinement phenomena it is important to understand how do the abelian monopoles arise in the non-abelian gauge theories.…”

Section: §1 Introductionmentioning

confidence: 99%

Monopoles in the Abelian Projection of Gluodynamics

Chernodub

Gubarev

Polikarpov

et al. 1998

Prog. Theor. Phys. Suppl.

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“…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].…”

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confidence: 99%

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

et al. 2007

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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...

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“…5,6,7 The tube appears due to a dual analogue of the Meissner effect: the (chromo)electric field of the quarks is squeezed into the flux tube as a result of the condensation of the Abelian monopoles (for a review see Refs. 11,12).…”

Section: Introductionmentioning

confidence: 99%

Monopoles From Quark Condensates in QCD

Chernodub

2008

Mod. Phys. Lett. A

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Chiral monopoles are hedgehoglike structures in local chiral condensates in QCD. These monopoles are (i) made of quark and gluon fields; (ii) explicitly gauge-invariant; and (iii) they carry quantized and conserved chromomagnetic charge. We argue that the chiral condensate vanishes in a core of the chiral monopole while the density of these monopoles increases with temperature wiping out the quark condensate in quark-gluon plasma. We suggest that the dynamics of the chiral monopoles is responsible for the chiral symmetry restoration in high temperature phase of QCD. We also argue that the chiral monopoles are unlikely to be associated with confining degrees of freedom. In our approach the chiral symmetry restoration and the color deconfinement in QCD are not necessarily related to each other and the corresponding transitions may occur at different temperatures.

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Abelian Projections and Monopoles

Cited by 59 publications

References 45 publications

Monopoles in the Abelian Projection of Gluodynamics

Monopoles in the Abelian Projection of Gluodynamics

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

Monopoles From Quark Condensates in QCD

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