Instanton, Monopole Condensation and Confinement

The confinement mechanism in the nonperturbative QCD is studied in terms of topological excitation as QCD-monopoles and instantons. In the 't Hooft abelian gauge, QCD is reduced into an abelian gauge theory with monopoles, and the QCD vacuum can be regarded as the dual superconductor with monopole condensation, which leads to the dual Higgs mechanism. The monopole-current theory extracted from QCD is found to have essential features of confinement. We find also close relation between monopoles and instantons using the lattice QCD. In this framework, the lowest $0^{++}$ glueball (1.5 $\sim$ 1.7GeV) can be identified as the QCD-monopole or the dual Higgs particle.Comment: Talk presented by H.Suganuma at the 5th Topical Seminar on The Irresistible Rise of the Standard Model, San Miniato al Todesco, Italy, 21-25 April 1997 5 pages, Plain Late

Confinement Properties in the Multi-Instanton System

We investigate the confinement properties in the multi-instanton system, where the size distribution is assumed to be $\rho^{-5}$ for the large instanton size $\rho$. We find that the instanton vacuum gives the area law behavior of the Wilson loop, which indicates existence of the linear confining potential. In the multi-instanton system, the string tension increases monotonously with the instanton density, and takes the standard value $\sigma \simeq 1 GeV/fm$ for the density $(N/V)^{{1/4}} = 200 MeV$. Thus, instantons directly relate to color confinement properties.Comment: Talk presented by M. Fukushima at ``Lattice '97'', the International Symposium on Lattice Field Theory, 22 - 26 July 1997, in Edinburgh, Scotland, 3 pages, Plain Late

Instanton and Monopole in External Chromomagnetic Fields

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

Relation between Confinement and Chiral Symmetry Breaking in Temporally Odd-number Lattice QCD

In the lattice QCD formalism, we investigate the relation between confinement and chiral symmetry breaking. A gauge-invariant analytical relation connecting the Polyakov loop and the Dirac modes is derived on a temporally odd-number lattice, where the temporal lattice size is odd, with the normal (nontwisted) periodic boundary condition for link-variables. This analytical relation indicates that low-lying Dirac modes have little contribution to the Polyakov loop, and it is numerically confirmed at the quenched level in both confinement and deconfinement phases. This fact indicates no direct one-to-one correspondence between confinement and chiral symmetry breaking in QCD. Using the relation, we also investigate the contribution from each Dirac mode to the Polyakov loop. In the confinement phase, we find a new "positive/negative symmetry" of the Dirac-mode matrix element of the link-variable operator, and this symmetry leads to the zero value of the Polyakov loop. In the deconfinement phase, there is no such symmetry and the Polyakov loop is nonzero. Also, we develop a new method for spin-diagonalizing the Dirac operator on the temporally odd-number lattice modifying the Kogut-Susskind formalism.Comment: 15pages, 9 figure

Clustering of Monopoles in the Instanton Vacuum

We generate a random instanton vacuum with various densities and size distributions. We perform numerically the maximally abelian gauge fixing of these configurations in order to find monopole trajectories induced by instantons. We find that instanton-induced monopole loops form enormous clusters occupying the whole physical volume, provided instantons are sufficiently dense. It indicates that confinement might be caused by instantons.Comment: 7 pages, Plain Latex, (3 figures - available on request from [email protected]

Proposal for exotic-hadron search by fragmentation functions

It is proposed that fragmentation functions should be used to identify exotic hadrons. As an example, fragmentation functions of the scalar meson f_0(980) are investigated. It is pointed out that the second moments and functional forms of the u- and s-quark fragmentation functions can distinguish the tetraquark structure from $q\bar q$. By the global analysis of f_0 (980) production data in electron-positron annihilation, its fragmentation functions and their uncertainties are determined. It is found that the current available data are not sufficient to determine its internal structure, while precise data in future should be able to identify exotic quark configurations.Comment: 4 pages, 4 figures, revtex, To be published in PR

Quark tensor charge and electric dipole moment within the Schwinger-Dyson formalism

We calculate the tensor charge of the quark in the QCD-like theory in the Landau gauge using the Schwinger-Dyson formalism. It is found that the dressed tensor charge of the quark is significantly suppressed against the bare quark contribution, and the result agrees qualitatively with the analyses in the collinear factorization approach and lattice QCD. We also analyze the quark confinement effect with the phenomenological strong coupling given by Richardson, and find that this contribution is small. We show that the suppression of the quark tensor charge is due to the superposition of the spin flip of the quark arising from the successive emission of gluons which dress the tensor vertex. We also consider the relation between the quark and the nucleon electric dipole moments by combining with the simple constituent quark model.Comment: 16 pages, 11 figures. arXiv admin note: text overlap with arXiv:1401.285

Some Relations for Quark Confinement and Chiral Symmetry Breaking in QCD

We analytically study the relation between quark confinement and spontaneous chiral-symmetry breaking in QCD. In terms of the Dirac eigenmodes, we derive some formulae for the Polyakov loop, its fluctuations, and the string tension from the Wilson loop. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clover and the domain wall fermion kernels, respectively. For the confinement quantities, the low-lying Dirac/fermion eigenmodes are found to give negligible contribution, while they are essential for chiral symmetry breaking. These relations indicate no direct one-to-one correspondence between confinement and chiral symmetry breaking in QCD, which seems to be natural because confinement is realized independently of the quark mass