Dual Meissner Effect and Magnetic Displacement Currents

Suzuki, Tsuneo; Ishiguro, Katsuya; Mori, Yoshihiro; Sekido, Toru

doi:10.1103/physrevlett.94.132001

Cited by 49 publications

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“…[22] where the Landau (LA) gauge is considered and for Abelian components the dual Meissner effect is observed. A magnetic displacement current plays the role of the solenoidal supercurrent which squeezes the Abelian electric fields, although the density of DeGrand-Toussaint monopoles [23] is very small in the LA gauge.…”

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confidence: 99%

Vacuum type of SU(2) gluodynamics in maximally Abelian and Landau gauges

et al. 2005

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The vacuum type of SU(2) gluodynamics is studied using Monte Carlo simulations in maximally Abelian (MA) gauge and in Landau (LA) gauge, where the dual Meissner effect is observed to work. The dual Meissner effect is characterized by the coherence and the penetration lengths. Correlations between Wilson loops and electric fields are evaluated in order to measure the penetration length in both gauges. The coherence length is shown to be fixed in the MA gauge from measurements of the monopole density around the static quark-antiquark pair. It is also shown numerically that a dimension 2 gluon operator A A ÿ s and the monopole density has a strong correlation as suggested theoretically. Such a correlation is observed also between the monopole density and A 2 s A A ÿ s A 3 A 3 s condensate if the remaining U(1) gauge degree of freedom is fixed to U(1) Landau gauge (U1LA). The coherence length is determined numerically also from correlations between Wilson loops and A A ÿ s and A 2 s in MA U1LA gauge. Assuming that the same physics works in the LA gauge, we determine the coherence length from correlations between Wilson loops and A 2 s . Penetration lengths and coherence lengths in the two gauges are almost the same. The vacuum type of the confinement phase in both gauges is near to the border between the type 1 and the type 2 dual superconductors.

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Section: Introductionmentioning

confidence: 99%

Vacuum type of SU(2) gluodynamics in maximally Abelian and Landau gauges

et al. 2005

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“…Next let us study the dual Meissner effect in local unitary gauges. In this calculation, we employ the improved Iwasaki gauge action with the coupling constant β = 1.20, which corresponds to the lattice spacing a(β) = 0.0792(2) fm [27]. The lattice size is 32 4 with periodic boundary conditions.…”

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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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“…Note that relation (18) makes it possible to rewrite the OZF free energy as a more complicated (compared to (20)) expression in terms of the order parameterQ. The YM theory (14)(15)(16)(17) can be associated with a nematic crystal in which the "molecules" are directed in the internal SO(3) int space. There are three species of equivalent molecules in each space-time point (the number of species equals to the number of the gluons, N c = 3).…”

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“…(16), it can be interpreted as an energy density associated with a mutual non-alignment of the directions of the different molecule species (Φ a ) i (x)/|Φ a (x)|. Let us find the ground state of the nematic associated with the YM theory (15,16,17). In terms of the eigenvalues of the matrix χ = diag(χ 1 , χ 2 , χ 3 ), the ground state χ = χ (0) is defined by the relations:…”

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Yang–Mills theory in Landau gauge as a liquid crystal

Chernodub¹

2006

Physics Letters B

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Using a spin-charge separation of the gluon field in the Landau gauge we show that the SU (2) Yang-Mills theory in the low-temperature phase can be considered as a nematic liquid crystal. The ground state of the nematic crystal is characterized by the A 2 condensate of the gluon field. The liquid crystal possesses various topological defects (instantons, monopoles and vortices) which are suggested to play a role in non-perturbative features of the theory.Separation of degrees of freedom is a useful analytical tool which is widely used in various physical applications. For example, the spin-charge decomposition (often referred to as the slave-boson formalism [1]) of the strongly correlated electrons is a popular technique invoked to describe a low-temperature physics of the high-T c cuprate superconductors [2]. According to the slave-boson formalism the electron creation operator c † iσ is represented as the product of two operators,where i is the lattice site and σ =↑, ↓ is the spin index. The operator f † iσ creates a chargeless spin-1/2 fermion state ("spinon") while the operator b i annihilates a charged spin-0 boson state ("holon"). Physically, the electron is represented as a composite of the spinon particle (which carries information about the spin of the electron) and the holon particle (which knows about the electron charge). The decomposition conserves the total number of the degrees of freedom because of the constraint(1) the states with double occupancy are disregarded for simplicity.The local nature of the spin-charge decomposition (1) leads to an emergence of an internal compact U(1) gauge symmetry realized in the form of the gauge transformationsCertain properties of the high-T c superconductors can be described [2,3] by U(1) gauge models which are utilizing the mentioned internal gauge symmetry. These gauge models are treatable within the mean field approach which predicts a rich phase structure. In particular, the d-wave high-T c superconductor is suggested [3] to be realized as a phase in which the spinon pairing,, is accompanied with a spontaneous breaking of the internal U(1) symmetry by the holon condensate:The presence and the subsequent spontaneous breaking of the internal gauge symmetry may have important physical consequences if even this symmetry is not realized in the original formulation of the theory. Quantum Chromodynamics is another example of a strongly interacting system in which the breaking of the internal symmetry may play an essential role. Long time ago it was

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Dual Meissner Effect and Magnetic Displacement Currents

Cited by 49 publications

References 33 publications

Vacuum type of SU(2) gluodynamics in maximally Abelian and Landau gauges

Vacuum type of SU(2) gluodynamics in maximally Abelian and Landau gauges

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

Yang–Mills theory in Landau gauge as a liquid crystal

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