arXiv subjects
Publications and source records attributed to Yoshimi Matsubara.
We calculate inter-meson potentials numerically by solving classical equations of motion derived from Dual Ginzburg-Landau (DGL) Theory. Inter-meson potentials in DGL theory are shown to be similar to those of the string-flip model and well reproduce behaviors of the short-range interaction at the classical level. We also compare our results with those from lattice QCD Monte carlo calculations.
Effective monopole actions for various extended monopoles are derived from vacuum configurations after abelian projection in the maximally abelian gauge in $T=0$ and $T\ne 0$ $SU(3)$ lattice QCD. The actions obtained appear to be independent of the lattice volume adopted. At zero temperature, monopole condensation is seen to occur from energy-entropy balance in the strong coupling region. Larger $β$ is included in the monopole condensed phase as more extended monopoles are considered. The scaling seen in the $SU(2)$ case is not yet observed. The renormalization flow diagram suggests the existence of an infrared fixed point. A hysteresis behavior is seen around the critical temperature in the case of the $T\ne 0$ action.
The disorder parameter of confinement-deconfinement phase transition based on the monopole action determined previously in $SU(2)$ QCD are investigated. We construct an operator which corresponds to the order parameter defined in the abelian Higgs model. The operator shows proper behaviors as the disorder parameter in the numerical simulations of finite temperature QCD.
Three topics about monopole dynamics after abelian projection are reported. The first is the new and detailed analyses of $SU(2)$ monopole action obtained after the block-spin transformation on the dual lattice. The $b=na(β)$ dependence for all couplings are well fitted with a universal curve. The distance dependence of the couplings is well reproduced by a massive propagator with the mass $m=0.8$ in unit of $b$. The second is the $SU(3)$ monopole action recently obtained. The third is new interesting gauges showing abelian and monopole dominances as in the maximally abelian gauge.
To find a perfect lattice action in terms of monopole action on the dual lattice, we performed simulations of a monopole effective action obtained numerically from vacuum configurations in SU(2) QCD. Although the Polyakov loop behavior near $T_c$ is well reproduced by the action, a small but repulsive term is needed in addition to get the string tension correctly. It is reported also a monopole effective action in $SU(3)$ QCD which is expressed by one kind of monopole currents.
We investigated the gauge (in)dependence of the confinement mechanism due to monopole condensation in SU(2) lattice QCD by various abelian projections. We found (1) the string tension can be reproduced by monopoles alone also in Polyakov gauge and (2) the behaviors of the Polyakov loop at the critical temperature seem to be explained by the uniformity breaking of the monopole currents in every gauge.
We investigate the role of monopoles in the deconfinement transition of finite temperature $SU(2)$ QCD in the maximally abelian gauge. In the confinement phase a long monopole loop exists in each configuration, whereas no long loop exists in the deep deconfinement region. Balancing of the energy and the entropy of loops of the maximally extended monopoles can explain the occurrence of the deconfinement transition.
Monte-Carlo simulations of abelian projection in $T \neq 0$ pure lattice QCD show that 1)\ Polyakov loops written in terms of abelian link fields alone play a role of an order parameter of deconfinement transition 2)\ the abelian Polyakov loops are decomposed into contributions from Dirac strings of monopoles and from photons 3)\ vanishing of the abelian Polyakov loops in the confinement phase is due to the Dirac strings alone and the photons give a finite contribution in both phases. Moreover, these results appear to hold good in unitary gauges. This suggests that monopole condensation as the color confinement mechanism is gauge independent.
Monopole and photon contributions to abelian Wilson loops are calculated using Monte-Carlo simulations of finite-temperature $SU(2)$ QCD in the maximally abelian gauge. The string tension is reproduced by monopole contribution alone also in finite temperature SU(2) QCD. The spatial string tension scales as $\sqrtσ \propto g^{2}(T)T$ and is reproduced almost by monopole contribution alone. Each configuration has one long monopole loop, and the long monopole loops alone are responsible for the string tension in the confinement phase. On the other hand, the spatial string tension in the deconfinement phase is reproduced by wrapped monopole loops alone.
The role of monopoles in the deconfinement transition is discussed in the framework of abelian projection in the maximally abelian gauge in $T\neq0$ $SU(2)$ QCD. Only one (or a few near $β_c$) long connected monopole loop exists uniformly through the whole lattice in each vacuum configuration in addition to some very short loops in the confinement phase and the long loop disappears in the deep deconfinement region. Energy-entropy balance of the long loops of maximally extended monopoles explains the existence of the deconfinement transition and reproduces roughly the value of the critical temperature.
Monte-Carlo simulations of abelian projection of $T \neq 0$ pure lattice QCD show that 1) Polyakov loops written in terms of abelian link fields alone play a role of an order parameter of deconfinement transition, 2) the abelian Polyakov loops are decomposed into contributions from Dirac strings of monopoles and from photons, 3) vanishing of the abelian Polyakov loops in the confinement phase is due to the Dirac strings alone and the photons give a finite contribution in both phases. Moreover, these results appear to hold good with any abelian projection as seen from the studies in the maximally abelian gauge and in various unitary gauges.
Monopole and photon contributions to abelian Wilson loops are calculated using Monte-Carlo simulations of finite-temperature $SU(2)$ QCD in the maximally abelian gauge. Long monopole loops alone are responsible for the behavior of the string tension in the confinement phase up to the critical $β_c$. Short monopole loops and photons do not contribute to the string tension. The abelian and the monopole spacial string tensions (both of which agree with the normal ones for $β< β_c$) show a $g^{4}(T) T^2$ scaling behavior in the deconfinement phase. The abelian spacial string tension is in agreement with the full one even in the deconfinement phase.