Dual superconductivity in the SU(2) pure gauge vacuum: A lattice study

Cea, Paolo; Cosmai, Leonardo

doi:10.1103/physrevd.52.5152

Cited by 81 publications

(124 citation statements)

References 32 publications

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“…This method does not change the behavior of the gauge field in the long distance, but it gives a finite value for the gauge field even at the origin. Therefore, we can obtain the formula which is valid for any distance (core radius) y from the axis connecting q andq: the profile of chromoelectric field in the dual superconductor is obtained: 191) provided that the scalar field is given by (See the right panel of Fig.57) 192) where K ν is the modified Bessel function of the ν-th order, λ the parameter corresponding to the London penetration length, ζ a variational parameter for the core radius, and Φ external electric flux. In the dual superconductor, we define the GL parameter κ as the ratio of the London penetration length λ and the coherence length ξ which measures the coherence of the magnetic monopole condensate (the dual version of the Cooper pair condensate): (9.192), together with the chromoelectric field E z (y).…”

Section: Type Of Dual Superconductivitymentioning

confidence: 99%

“…This is a nontrivial issue. In order to define the gauge-invariant chromofield strength tensor, we introduce the following 224 operator representing a gauge-invariant connected correlator between the Wilson loop operator and a plaquette variable according to Di Giacomo, Maggiore and Olejnik [191,192]: 111) where W is the Wilson loop operator representing a pair of quark and antiquark, U P is the plaquette variable as the probe for measuring the chromofield strength at the position of the plaquette, and L is the line connecting the plaquette U P and the Wilson loop operator W , which is called the Schwinger line. See Fig.…”

Section: Chromoelectric Field and Flux Tube Formationmentioning

confidence: 99%

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Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang–Mills theory

et al. 2015

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The purpose of this paper is to review the recent progress in understanding quark confinement. The emphasis of this review is placed on how to obtain a manifestly gauge-independent picture for quark confinement supporting the dual superconductivity in the Yang-Mills theory, which should be compared with the Abelian projection proposed by 't Hooft. The basic tools are novel reformulations of the YangMills theory based on change of variables extending the decomposition of the SU(N) Yang-Mills field due to Cho, Duan-Ge and Faddeev-Niemi, together with the combined use of extended versions of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the SU(N) Wilson loop operator.Moreover, we give the lattice gauge theoretical versions of the reformulation of the Yang-Mills theory which enables us to perform the numerical simulations on the lattice. In fact, we present some numerical evidences for supporting the dual superconductivity for quark confinement. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the "Abelian" dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc. In addition, we give a direct connection between the topological configuration of the Yang-Mills field such as instantons/merons and the magnetic monopole.We show especially that magnetic monopoles in the Yang-Mills theory can be constructed in a manifestly gauge-invariant way starting from the gauge-invariant Wilson loop operator and thereby the contribution from the magnetic monopoles can be extracted from the Wilson loop in a gauge-invariant way through the non-Abelian Stokes theorem for the Wilson loop operator, which is a prerequisite for exhibiting magnetic monopole dominance for quark confinement. The Wilson loop average is calculated according to the new reformulation written in terms of new field variables obtained from the original Yang-Mills field based on change of variables. The Maximally Abelian gauge in the original Yang-Mills theory is also reproduced by taking a specific gauge fixing in the reformulated Yang-Mills theory. This observation justifies the preceding results obtained in the maximal Abelian gauge at least for gaugeinvariant quantities for SU(2) gauge group, which eliminates the criticism of gauge artifact raised for the Abelian projection. The claim has been confirmed based on the numerical simulations.However, for SU(N) (N ≥ 3), such a gauge-invariant reformulation is not unique, although the extension along the line proposed by Cho, Faddeev and Niemi is possible. In fact, we have found that there are a number of possible options of the reformulations, which are discriminated by the maximal stability 1 groupH of G, while there is a unique option ofH = U(1) for G = SU(2). The maximal stability group depends...

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Section: Type Of Dual Superconductivitymentioning

confidence: 99%

Section: Chromoelectric Field and Flux Tube Formationmentioning

confidence: 99%

Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang–Mills theory

et al. 2015

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“…All of these facts support the conjecture that the color confinement is due to the dual Meissner effect caused by the monopole condensation. Numerical calculations show that the vacuum of quenched SU(2) QCD [SU (2) gluodynamics] is near the border between the type 1 and the type 2 dual superconductor [10,[13][14][15][16], although there are some claims that it is a superconductor of weakly type 1, see Refs. [9,17,18].…”

Section: Introductionmentioning

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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“…Indeed, Monte Carlo simulations produce samples of vacuum configurations that, in principle, contain all the relevant information on the nonperturbative sector of QCD. A wealth of numerical analyses in QCD has firmly established that the chromoelectric field between a static quark-antiquark pair distributes in tubelike structures or "flux tubes" [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. From these tubelike structures a linear potential between static color charges naturally arises, thus representing a numerical evidence of color confinement.…”

Section: Introductionmentioning

confidence: 99%