Gauge invariance of color confinement due to the dual Meissner effect caused by Abelian monopoles

Suzuki, Tsuneo; Hasegawa, Masayasu; Ishiguro, Katsuya; Koma, Yoshiaki; Sekido, Toru

doi:10.1103/physrevd.80.054504

Cited by 38 publications

(91 citation statements)

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“…al [35] suggests κ = 0.5 ∼ 1(which is β dependent), border of type I and type II for both SU (2) and SU (3). In SU (2) case, on the other hand, there are other works [33,34] which conclude that the type of vacuum is at the border of type I and type II.…”

Section: Type Of Dual Superconductivitymentioning

confidence: 99%

“…The chromo-flux of the Yang-Mills field has been already measured by using a gauge-invariant Wilson line/loop operator [28] by the preceding works: [29][30][31][32][33][34][35][36] for SU (2) case and for the SU (3) case. However, most of the SU (2) case were done using the Abelian projection and there were no direct measurement of the dual Meissner effect in the gauge independent (invariant) way, except for quite recent studies [36,38,52].…”

Section: Introductionmentioning

confidence: 99%

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Non-Abelian dual superconductivity inSU(3)Yang-Mills theory: Dual Meissner effect and type of the vacuum

et al. 2013

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We have proposed the non-Abelian dual superconductivity picture for quark confinement in the SU (3) Yang-Mills (YM) theory, and have given numerical evidences for the restricted-field dominance and the non-Abelian magnetic monopole dominance in the string tension by applying a new formulation of the YM theory on a lattice. To establish the non-Abelian dual superconductivity picture for quark confinement, we have observed the non-Abelian dual Meissner effect in the SU (3) Yang-Mills theory by measuring the chromoelectric flux created by the quark-antiquark source, and the non-Abelian magnetic monopole currents induced around the flux. We conclude that the dual superconductivity of the SU (3) Yang-Mills theory is strictly the type I and that this type of dual superconductivity is reproduced by the restricted field and the non-Abelian magnetic monopole part, in sharp contrast to the SU (2) case: the border of type I and type II.

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Section: Type Of Dual Superconductivitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Non-Abelian dual superconductivity inSU(3)Yang-Mills theory: Dual Meissner effect and type of the vacuum

et al. 2013

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“…al [204] suggests κ = 0.5 ∼ 1(which is β dependent), border of type I and type II for both SU(2) and SU(3). In SU(2) case, on the other hand, there are other works [206,205] which conclude that the type of vacuum is at the border of type I and type II. Our results [29] are consistent with the border of type I and type II for the SU(2) Yang-Mills theory on the lattice, as already shown in the above.…”

Section: Type Of Dual Superconductivitymentioning

confidence: 99%

“…The correlation functions (propagators) of the original Yang-Mills field and the new variables are defined by 206) where an operator O µ (x) = O A µ (x)T A is defined as the linear type, e.g., A x ′ ,µ = U x,µ − U † x,µ / (2iεg). The right panel of Fig.…”

Section: Numerical Simulations In the Maximal Option Of Su(3)mentioning

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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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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“…Recently, we obtained clear numerical evidences of Abelian dominance and the dual Meissner effect in local unitary gauges [21] and without adopting gauge fixing [22,23] in SU(2) lattice gauge theory, where we have used the DeGrand-Toussaint monopoles [6] as in the MA gauge. These results provide us with the following idea ; there must exist a gauge-invariant mechanism of color confinement due to Abelian monopoles [24,25].…”

Section: Introductionmentioning

confidence: 99%

Gauge invariance of the color confinement mechanism due to the Abelian dual Meissner effect

Ishiguro¹

2010

Proceedings of the XXVII International Symposium on Lattice Field Theory — PoS(LAT2009)

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The mechanism of non-Abelian color confinement is studied in SU(2) lattice gauge theory in terms of the Abelian fields and monopoles extracted from non-Abelian link variables without adopting gauge fixing. First, the static quark-antiquark potential and force are computed with the Abelian and monopole Polyakov loop correlators, and the resulting string tensions are found to be identical to the non-Abelian string tension. These potentials also show the scaling behavior with respect to the change of lattice spacing. Second, the profile of the color-electric field between a quark and an antiquark is investigated with the Abelian and monopole Wilson loops. The colorelectric field is squeezed into a flux tube due to monopole supercurrent with the same Abelian color direction. The parameters corresponding to the penetration and coherence lengths show the scaling behavior, and the ratio of these lengths, i.e., the Ginzburg-Landau parameter, indicates that the vacuum type is near the border of the type 1 and type 2 (dual) superconductors. These results are summarized in which the Abelian fundamental charge defined in an arbitrary color direction is confined inside a hadronic state by the dual Meissner effect. As the color-neutral state in any Abelian color direction corresponds to the physical color-singlet state, this effect explains non-Abelian color confinement and supports the existence of a gauge-invariant mechanism of color confinement due to the dual Meissner effect caused by Abelian monopoles. The XXVII International Symposium on Lattice Field Theory

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Gauge invariance of color confinement due to the dual Meissner effect caused by Abelian monopoles

Cited by 38 publications

References 50 publications

Non-Abelian dual superconductivity inSU(3)Yang-Mills theory: Dual Meissner effect and type of the vacuum

Non-Abelian dual superconductivity inSU(3)Yang-Mills theory: Dual Meissner effect and type of the vacuum

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

Gauge invariance of the color confinement mechanism due to the Abelian dual Meissner effect

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