Monopole clustering and color confinement in the multi-instanton system

Fukushima, Masahiro; Suganuma, Hideo; Toki, H.

doi:10.1103/physrevd.60.094504

Cited by 11 publications

(21 citation statements)

References 67 publications

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“…This parallels the previous observation in Ref. [3] that blocking of monopole currents is necessary to see percolation/condensation happening. Glance into a time-slice of a typical configuration with continuum instantons (balls) and lattice monopoles (bars) living on the coarsest lattice (with lattice spacing a = 0.8 fm).…”

Section: Discussionsupporting

confidence: 91%

“…Very recently, in Ref. [38], a distribution like (3) has been demonstrated to emerge, in dimension d > 2, from a very general model of soft (inflatable) spheres with excluded-volume interaction which inherits from QCD not more than the semiclassical perturbative instanton fugacity proportional to ρ b−5 . In the grand canonical Monte Carlo simulation of this system the ρ dependent fugacity has been used in conjunction with the excluded-volume constraint.…”

Section: Continuum Multi-instanton Configurations and Their Discrmentioning

confidence: 99%

“…[11][12][13]). Different groups roughly agree on the size of instantons within a factor of two, e.g.ρ = 0.3...0.6 fm for SU (3). There is no agreement at all concerning the density N/V which is strongly dependent on the procedure to remove size O(a) vacuum fluctuations (cooling, smoothing etc.)…”

Section: Introductionmentioning

confidence: 97%

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Abelian monopole and center vortex views at the multi-instanton gas

2001

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We consider full non-Abelian, Abelian and center projected lattice field configurations built up from random instanton gas configurations in the continuum. We study the instanton contribution to theQQ force with respect to (i) instanton density dependence, (ii) Casimir scaling and (iii) whether various versions of Abelian dominance hold. We check that the dilute gas formulation for the interaction potential gives an reliable approximation only for densities small compared to the phenomenological value. We find that Casimir scaling does not hold, confirming earlier statements in the literature. We show that the lattice used to discretize the instanton gas configurations has to be sufficiently coarse (a ≈ 2ρ compared with the instanton sizeρ) such that maximal Abelian gauge projection and center projection as well as the monopole gas contribution to theQQ force reproduce the non-Abelian instantonmediated force in the intermediate range of linear quasi-confinement. We demonstrate that monopole clustering also depends critically on the discretization scale confirming earlier findings based on monopole blocking. Sometimes the density N/V = 1 fm −4 is used as a criterium to stop cooling, in this way

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Section: Discussionsupporting

confidence: 91%

Section: Continuum Multi-instanton Configurations and Their Discrmentioning

confidence: 99%

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Abelian monopole and center vortex views at the multi-instanton gas

2001

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“…21) - 26) This correspondence may provide a scenario of a color confinement mechanism that the instanton fields give rise to the multi-production of monopole loops as a signal of monopole condensation. 24), 25) For this reason, we further investigate the appearance of monopoles around the instanton as a deformed configuration in external color magnetic fields. §2.…”

Section: §1 Introductionmentioning

confidence: 99%

Instanton and Monopole in External Chromomagnetic Fields

Fukushima¹,

Suganuma²,

Chiba³

2002

Progress of Theoretical Physics

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We study properties of instanton and monopole in an external chromomagnetic field. Generally, the 't Hooft ansatz is no longer a solution of the Yang-Mills field equation in the presence of external fields. Therefore, we investigate a stabilized instanton solution with minimal total Yang-Mills action in a nontrivial topological sector. With this aim, we consider numerical minimization of the action with respect to the global color orientation, the anisotropic scale transformation and the local gauge-like transformation starting from a simple superposed gauge field of the 't Hooft ansatz and the external color field. Here, the external color field is, for simplicity, chosen to be a constant Abelian magnetic field along a certain direction. Then, the 4-dimensional rotational symmetry O(4) of the instanton solution is reduced to two 2-dimensional rotational symmetries $O(2)\times O(2)$ due to the effect of a homogeneous external field. In the space $\mib{R}^{3}$ at fixed $t$, we find a quadrupole deformation of this instanton solution. In the presence of a magnetic field $\vec{H}$, a prolate deformation occurs along the direction of $\vec{H}$. Contrastingly, in the presence of an electric field $\vec{E}$ an oblate deformation occurs along the direction of $\vec{E}$. We further discuss the local correlation between the instanton and the monopole in the external field in the maximally Abelian gauge. The external field affects the appearance of the monopole trajectory around the instanton. In fact, a monopole and anti-monopole pair appears around the instanton center, and this monopole loop seems to partially screen the external field.Comment: 15 pages,8 figure

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“…From the concentration of off-diagonal gluons around QCD-monopoles in the MA gauge, we can predict a local correlation between monopoles and instantons: instantons tend to appear around the monopole world-line in the MA gauge, because instantons need full SU(2) gluon components for existence [9][10][11][18][19][20][21].…”

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confidence: 99%

Hadron Physics and Confinement Physics in Lattice QCD

Suganuma¹,

Amemiya²,

Ichie³

et al. 2001

AIP Conference Proceedings

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We are aiming to construct Quark Hadron Physics and Confinement Physics based on QCD. Using SU(3) c lattice QCD, we are investigating the three-quark potential at T = 0 and T = 0, mass spectra of positive and negative-parity baryons in the octet and the decuplet representations of the SU(3) flavor, glueball properties at T = 0 and T = 0. We study also Confinement Physics using lattice QCD. In the maximally abelian (MA) gauge, the off-diagonal gluon amplitude is strongly suppressed, and then the off-diagonal gluon phase shows strong randomness, which leads to a large effective off-diagonal gluon mass, M off ≃ 1.2GeV. Due to the large off-diagonal gluon mass in the MA gauge, infrared QCD is abelianized like nonabelian Higgs theories. In the MA gauge, there appears a macroscopic network of the monopole world-line covering the whole system. From the monopole current, we extract the dual gluon field B µ , and examine the longitudinal magnetic screening. We obtain m B ≃ 0.5 GeV in the infrared region, which indicates the dual Higgs mechanism by monopole condensation. From infrared abelian dominance and infrared monopole condensation, low-energy QCD in the MA gauge is described with the dual Ginzburg-Landau (DGL) theory. Quark Hadron Physics from Lattice QCDQuantum chromodynamics (QCD) established as the fundamental theory of the strong interaction takes a simple form [ 1,2],however, it is still hard to understand nonperturbative phenomena, such as color confinement and dynamical chiral-symmetry breaking, due to the infrared strong-coupling feature [ 1,2]. In this decade, lattice QCD Monte Carlo calculations have been developed and have been mainly applied to (i) hadron spectroscopy and (ii) finite temperature QCD phase transition, with a great success. However, lattice QCD is applicable also to (iii) Quark Hadron Physics and (iv) Confinement Physics, as a useful and reliable method. Our group is aiming to construct Quark Hadron Physics and Confinement Physics based on lattice QCD. Our strategy is to adopt lattice QCD calculations to the relevant

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Monopole clustering and color confinement in the multi-instanton system

Cited by 11 publications

References 67 publications

Abelian monopole and center vortex views at the multi-instanton gas

Abelian monopole and center vortex views at the multi-instanton gas

Instanton and Monopole in External Chromomagnetic Fields

Hadron Physics and Confinement Physics in Lattice QCD

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