Polyakov loops and monopoles in QCD

Suzuki, Tsuneo; Ilyar, Sawut; Matsubara, Yoshimi; Okude, Tsuyoshi; Yotsuji, K.

doi:10.1016/0370-2693(95)00068-v

Cited by 40 publications

(36 citation statements)

References 21 publications

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“…For the results of numerical simulations for SU(3) Yang-Mills theory in the MA gauge, see e.g., [89,90,91,92,93,94,95,96]. However, we do not necessarily need to consider the maximal breaking SU(N) → U(1) N −1 , although the maximal torus group is desirable as a gauge group of the low-energy effective Abelian gauge theory [53].…”

Section: Abelian Dominance and Magnetic Monopole Dominancementioning

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: Abelian Dominance and Magnetic Monopole Dominancementioning

confidence: 99%

“…However, we cannot verify the smoothness by giving the value of the functional to be minimized, since it is difficult to obtain the data at the instance that a loop was just separated into two smaller loops. 89 …”

Section: Two Instantons and Magnetic Monopole Loops On The Latticementioning

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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“…We may decompose the Abelian gauge field into a monopole and photon part according to the definition [20,21] …”

Section: Comparison Of 3qmentioning

confidence: 99%

Baryonic flux in quenched and two-flavor dynamical QCD after Abelian projection

et al. 2004

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We study the distribution of color electric flux of the three-quark system in quenched and full QCD (with N f 2 flavors of dynamical quarks) at zero and finite temperature. To reduce ultraviolet fluctuations, the calculations are done in the Abelian projected theory fixed to the maximally Abelian gauge. In the confined phase we find clear evidence for a Y-shape flux tube surrounded and formed by the solenoidal monopole current, in accordance with the dual superconductor picture of confinement. In the deconfined, high temperature phase monopoles cease to condense, and the distribution of the color electric field becomes Coulomb-like.

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“…Since all the Polyakov loops can be exactly diagonalised at the same time, in this case "abelian dominance" exactly and trivially holds if the string tension is measured with Polyakov loop correlators. On the other hand due to the high level of noise on the projected configurations, it is impossible to extract the string tension from Wilson loops [5,6].…”

Section: Introductionmentioning

confidence: 99%

Remarks on Abelian dominance

Kovács

Schram

1997

Phys. Rev. D

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We used a renormalisation group based smoothing to address two questions related to abelian dominance. Smoothing drastically reduces short distance fluctuations but it preserves the long distance physical properties of the SU(2) configurations. This enabled us to extract the abelian heavy-quark potential from time-like Wilson loops on Polyakov gauge projected configurations. We obtained a very small string tension which is inconsistent with the string tension extracted from Polyakov loop correlators. This shows that the Polyakov gauge projected abelian configurations do not have a consistent physical meaning. We also applied the smoothing on SU(2) configurations to test how sensitive abelian dominance in the maximal abelian gauge is to the short distance fluctuations. We found that on smoothed SU(2) configurations the abelian string tension was about 30% smaller than the SU(2) string tension which was unaffected by smoothing. This suggests that the approximate abelian dominance found with the Wilson action is probably an accident and it has no fundamental physical relevance.

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Polyakov loops and monopoles in QCD

Cited by 40 publications

References 21 publications

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

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

Baryonic flux in quenched and two-flavor dynamical QCD after Abelian projection

Remarks on Abelian dominance

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