Evidence of Strong Correlation between Instanton and QCD-monopole on SU(2) Lattice

The correlation between instantons and QCD-monopoles is studied both in the lattice gauge theory and in the continuum theory. An analytical study in the Polyakov-like gauge, where $A_4(x)$ is diagonalized, shows that the QCD-monopole trajectory penetrates the center of each instanton, and becomes complicated in the multi-instanton system. Using the SU(2) lattice with $16^4$, the instanton number is measured in the singular (monopole-dominating) and regular (photon-dominating) parts, respectively. The monopole dominance for the topological charge is found both in the maximally abelian gauge and in the Polyakov gauge.Comment: 4 pages, Latex, 3 figures. Talk presented by H. Suganuma at International Symposium on 'Lattice Field Theory', July 11 - 15, 1995, Melbourne, Australi

A Conclusive Test of Abelian Dominance Hypothesis for Topological Charge in the QCD Vacuum

We study the topological feature in the QCD vacuum based on the hypothesis of abelian dominance. The topological charge $Q_{\rm SU(2)}$ can be explicitly represented in terms of the monopole current in the abelian dominated system. To appreciate its justification, we directly measure the corresponding topological charge $Q_{\rm Mono}$, which is reconstructed only from the monopole current and the abelian component of gauge fields, by using the Monte Carlo simulation on SU(2) lattice. We find that there exists a one-to-one correspondence between $Q_{\rm SU(2)}$ and $Q_{\rm Mono}$ in the maximally abelian gauge. Furthermore, $Q_{\rm Mono}$ is classified by approximately discrete values.Comment: LATTICE98(confine), 3 pages, Latex, 3 figures include

Simulation of SU(2) Dynamical Fermion at Finite Chemical Potential and at Finite Temperature

SU(2) lattice gauge theory with dynamical fermion at non-zero chemical potential and at finite temperature is studied. We focus on the influence of chemical potential for quark condensate and mass of pseudoscalar meson at finite temperature. Hybrid Monte Carlo simulations with $N_f=8$ staggered fermions are carried out on $12 \times 12\times 24 \times 4$ lattice. At $\beta=1.1$ and $m_{q}=$0.05,0.07,0.1, we calculate the quark condensate and masses of pseudoscalar meson consisting of light and heavier quarks for chemical potential $\mu=$ 0.0,0.02,0.05,0.1,0.2.Comment: Proceedings of the International Workshop on Nonperturbative Methods and Lattice QCD, Guangzhou, Chin

Monopole Current Dynamics and Color Confinement

Color confinement can be understood by the dual Higgs theory, where monopole condensation leads to the exclusion of the electric flux from the QCD vacuum. We study the role of the monopole for color confinement by investigating the monopole current system. When the self-energy of the monopole current is small enough, long and complicated monopole world-lines appear, which is a signal of monopole condensation. In the dense monopole system, the Wilson loop obeys the area-law, and the string tension and the monopole density have similar behavior as the function of the self-energy, which seems that monopole condensation leads to color confinement. On the long-distance physics, the monopole current system almost reproduces essential features of confinement properties in lattice QCD. In the short-distance physics, however, the monopole-current theory would become nonlocal and complicated due to the monopole size effect. This monopole size would provide a critical scale of QCD in terms of the dual Higgs mechanism.Comment: 6 pages LaTeX, 5 figures, uses espcrc1.sty, Talk presented at International Conference on Quark Lepton Nuclear Physics, Osaka, May. 199

Responses of quark condensates to the chemical potential

The responses of quark condensates to the chemical potential, as a function of temperature T and chemical potential \mu, are calculated within the Nambu--Jona-Lasinio (NJL) model. We compare our results with those from the recent lattice QCD simulations [QCD-TARO Collaboration, Nucl. Phys. B (Proc. Suppl.) 106, 462 (2002)]. The NJL model and lattice calculations show qualitatively similar behavior, and they will be complimentary ways to study hadrons at finite density. The behavior above T_c requires more elaborated analyses.Comment: 3 pages, 2 figs, based on a contribution to the Prof. Osamu Miyamura memorial symposium, Hiroshima University, Nov. 16-17, 2001; slightly revised, accepted for publication in Physical Review

Confinement and Topological Charge in the Abelian Gauge of QCD

We study the relation between instantons and monopoles in the abelian gauge. First, we investigate the monopole in the multi-instanton solution in the continuum Yang-Mills theory using the Polyakov gauge. At a large instanton density, the monopole trajectory becomes highly complicated, which can be regarded as a signal of monopole condensation. Second, we study instantons and monopoles in the SU(2) lattice gauge theory both in the maximally abelian (MA) gauge and in the Polyakov gauge. Using the $16^3 \times 4$ lattice, we find monopole dominance for instantons in the confinement phase even at finite temperatures. A linear-type correlation is found between the total monopole-loop length and the integral of the absolute value of the topological density (the total number of instantons and anti-instantons) in the MA gauge. We conjecture that instantons enhance the monopole-loop length and promote monopole condensation.Comment: 3 pages, LaTeX, Talk presented at LATTICE96(topology

Temporal meson correlators at finite temperature on quenched anisotropic lattice

We study charmonium correlators at finite temperature in quenched anisotropic lattice QCD. The smearing technique is applied to enhance the low energy part of the correlator. We use two analysis procedures: the maximum entropy method for extraction of the spectral function without assuming specific form, as an estimate of the shape of spectral function, and the $\chi^2$ fit assuming typical forms as quantitative evaluation of the parameters associated to the forms. We find that at $T\simeq 0.9T_c$ the ground state peak has almost the same mass as at T=0 and almost vanishing width. At $T\simeq 1.1T_c$, our result suggests that the correlator still has nontrivial peak structure at almost the same position as below $T_c$ with finite width.Comment: Lattice 2002 Nonzero temperature 3page