Dynamics of monopoles and flux tubes in two-flavor dynamical QCD

Bornyakov, V. G.; Ichie, H.; Koma, Yoshiaki; Mori, Yoshihiro; Nakamura, Y.; Pleiter, D.; Polikarpov, M. I.; Schierholz, G.; Streuer, T.; Stüben, H.; Suzuki, Tsuneo

doi:10.1103/physrevd.70.074511

Cited by 48 publications

(64 citation statements)

References 72 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%

“…93 iii) The covariant derivative D (ǫ) µ [V ] obeys the correct transformation property, i.e., the adjoint rotation on a lattice: 14) provided that the link variable V x,µ transforms in the same way as the original link variable U x,µ :…”

mentioning

confidence: 99%

“…In order to obtain the unique decomposition (9.4), we must fix the extra degrees of freedom by 93 Adopting another form instead of (9.13) using the ambiguity of O(ǫ 2 ), 0 = n x+µ −n x −iǫgV µ (x)n x +in x+µ ǫgV µ (x)+ O(ǫ 2 ), which is rewritten as…”

mentioning

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%

mentioning

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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“…To check that the monopoles are successfully added, we detect the monopoles in the configurations. It has been found that the monopoles are divided in two clusters [15,14,5,17] in MA gauge. The small (ultraviolet) clusters are composed of the short monopole loops.…”

Section: Zero Modes Of Overlap Fermions Instantons and Monopoles Mamentioning

confidence: 99%

“…The monopole creation operator is defined in [2,3,4]. (4) Measuring the additional monopoles We check whether the pair of monopoles is successfully added in the configurations or not, by use of the method developed in [5]. We find that adding one monopole-antimonopole pair makes one long monopole loop in configurations.…”

Section: (3) Additional Monopolesmentioning

confidence: 99%

Zero modes of overlap fermions, instantons and monopoles

Giacomo¹,

Hasegawa²

2015

Proceedings of the 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014)

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The purpose of this study is to investigate the relations between instantons, monopoles, and Chiral symmetry breaking. The monopoles are important topological configurations existing in QCD which are believed to produce colour confinement. The groups of University of Kanazawa and Pisa have produced by Lattice simulations many results supporting the idea that QCD vacuum is a dual superconductor. Instantons are related to Chiral symmetry breaking, as explained e.g. in the instanton liquid model of E. V. SHURYAK. Clarifying quantitatively the relation between monopoles and instantons is not easy, also because monopoles are three dimensional objects, while instantons are four dimensional. We generate configurations, adding monopoleantimonopole pairs of opposite charges by a monopole creation operator. We observe that the monopole creation operator only adds long monopole loops in the configurations. Then, we count the number of fermion zero modes in the configurations using Overlap fermions as a tool. Finally, we find that one monopole-antimonopole pair makes one zero mode of plus or minus chirality, that is to say, one instanton of plus or minus charge.

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Monopole and instanton effects in QCD

Hasegawa

2020

J. High Energ. Phys.

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We aim to show the effects of the magnetic monopoles and instantons in quantum chromodynamics (QCD) on observables; therefore, we introduce a monopole and anti-monopole pair in the QCD vacuum of a quenched SU(3) by applying the monopole creation operator to the vacuum. We calculate the eigenvalues and eigenvectors of the overlap Dirac operator that preserves the exact chiral symmetry in lattice gauge theory using these QCD vacua. We then investigate the effects of magnetic monopoles and instantons. First, we confirm the monopole effects as follows: (i) the monopole creation operator makes the monopoles and anti-monopoles in the QCD vacuum. (ii) A monopole and anti-monopole pair creates an instanton or anti-instanton without changing the structure of the QCD vacuum. (iii) The monopole and anti-monopole pairs change only the scale of the spectrum distribution without affecting the spectra of the Dirac operator by comparing the spectra with random matrix theory. Next, we find the instanton effects by increasing the number density of the instantons and anti-instantons as follows: (iv) the decay constants of the pseudoscalar increase. (v) The values of the chiral condensate, which are defined as negative numbers, decrease. (vi) The light quarks and the pseudoscalar mesons become heavy. The catalytic effect on the charged pion is estimated using the numerical results of the pion decay constant and the pion mass. (vii) The decay width of the charged pion becomes wider than the experimental result, and the lifetime of the charged pion becomes shorter than the experimental result. These are the effects of the monopoles and instantons in QCD.

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Dynamics of monopoles and flux tubes in two-flavor dynamical QCD

Cited by 48 publications

References 72 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

Zero modes of overlap fermions, instantons and monopoles

Monopole and instanton effects in QCD

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