Monopole Condensation in Lattice SU(2) QCD

This is the short review of Monte-Carlo studies of quark confinement in lattice QCD. After abelian projections both in the maximally abelian and Polyakov gauges, it is seen that the monopole part alone is responsible for confinement. A block spin transformation on the dual lattice suggests that lattice $SU(2)$ QCD is always ( for all $\beta$) in the monopole condensed phase and so in the confinement phase in the infinite volume limit.Comment: Contribution to Confinement '95, March 1995, Osaka, Japan. Names of figure files are corrected. 8 page uuencoded latex file and 10 ps figure

On the perfect lattice actions of abelian-projected SU(2) QCD

We study the perfect lattice actions of abelian-projected SU(2) gluodynamics. Using the BKT and duality transformations on the lattice, an effective string model is derived from the direction-dependent quadratic monopole action, obtained numerically from SU(2) gluodynamics in maximally abelian gauge. The string tension and the restoration of continuum rotational invariance are investigated using strong coupling expansion of lattice string model analytically. We also found that the block spin transformation can be performed analytically for the quadratic monopole action.Comment: 3 pages, Latex, 1 figures; talk presented at LATTICE9

Slow quench dynamics of the Kitaev model: anisotropic critical point and effect of disorder

We study the non-equilibrium slow dynamics for the Kitaev model both in the presence and the absence of disorder. For the case without disorder, we demonstrate, via an exact solution, that the model provides an example of a system with an anisotropic critical point and exhibits unusual scaling of defect density $n$ and residual energy $Q$ for a slow linear quench. We provide a general expression for the scaling of $n$ ($Q$) generated during a slow power-law dynamics, characterized by a rate $\tau^{-1}$ and exponent $\alpha$, from a gapped phase to an anisotropic quantum critical point in $d$ dimensions, for which the energy gap $\Delta_{\vec k} \sim k_i^z$ for $m$ momentum components ($i=1..m$) and $\sim k_i^{z'}$ for the rest $d-m$ components ($i=m+1..d$) with $z\le z'$: $n \sim \tau^{-[m + (d-m)z/z']\nu \alpha/(z\nu \alpha +1)}$ ($Q \sim \tau^{-[(m+z)+ (d-m)z/z']\nu \alpha/(z\nu \alpha +1)}$). These general expressions reproduce both the corresponding results for the Kitaev model as a special case for $d=z'=2$ and $m=z=\nu=1$ and the well-known scaling laws of $n$ and $Q$ for isotropic critical points for $z=z'$. We also present an exact computation of all non-zero, independent, multispin correlation functions of the Kitaev model for such a quench and discuss their spatial dependence. For the disordered Kitaev model, where the disorder is introduced via random choice of the link variables $D_n$ in the model's Fermionic representation, we find that $n \sim \tau^{-1/2}$ and $Q\sim \tau^{-1}$ ($Q\sim \tau^{-1/2}$) for a slow linear quench ending in the gapless (gapped) phase. We provide a qualitative explanation of such scaling.Comment: 10 pages, 11 Figs. v

Lattice monopole action in pure SU(3) QCD

We obtain an almost perfect monopole action numerically after abelian projection in pure SU(3) lattice QCD. Performing block-spin transformations on the dual lattice, the action fixed depends only on a physical scale b. Monopole condensation occurs for large b region. The numerical results show that two-point monopole interactions are dominant for large b. We next perform the block-spin transformation analytically in a simplified case of two-point monopole interactions with a Wilson loop on the fine lattice. The perfect operator evaluating the static quark potential on the coarse b-lattice are derived. The monopole partition function can be transformed into that of the string model. The static potential and the string tension are estimated in the string model framework. The rotational invariance of the static potential is recovered, but the string tension is a little larger than the physical one.Comment: 21pages,4figures,to be published in JHE

String tension and glueball masses of SU(2) QCD from perfect action for monopoles and strings

We study the perfect monopole action as an infrared effective theory of SU(2) QCD. It is transformed exactly into a lattice string model. Since the monopole interactions are weak in the infrared SU(2) QCD, the string interactions become strong. The strong coupling expansion of string model shows the quantum fluctuation is small. The classical string tension is estimated analytically, and we see it is very close to the quantum one in the SU(2) QCD. We also discuss how to calculate the glueball mass in our model.Comment: LATTICE99(Confinement), 3 pages and 1 EPS figure

Clustering of Far-Infrared Galaxies in the AKARI All-Sky Survey

We present the first measurement of the angular two-point correlation function for AKARI 90-$\mu$m point sources, detected outside of the Milky Way plane and other regions characterized by high Galactic extinction, and categorized as extragalactic sources according to our far-infrared-color based criterion (Pollo et al. 2010). This is the first measurement of the large-scale angular clustering of galaxies selected in the far-infrared after IRAS measurements. Although a full description of clustering properties of these galaxies will be obtained by more detailed studies, using either spatial correlation function, or better information about properties and at least photometric redshifts of these galaxies, the angular correlation function remains the first diagnostics to establish the clustering properties of the catalog and observed galaxy population. We find a non-zero clustering signal in both hemispheres extending up to $\sim 40$ degrees, without any significant fluctuations at larger scales. The observed correlation function is well fitted by a power law function. The notable differences between a northern and southern hemisphere are found, which can be probably attributed to the photometry problems and point out to a necessity of performing a better calibration in the data from southern hemisphere.Comment: 6 pages, 6 figures, accepted for publication in Earth, Planets, and Spac

Effective Monopole Action at Finite Temperature in SU(2) Gluodynamics

Effective monopole action at finite temperature in SU(2) gluodynamics is studied on anisotropic lattices. Using an inverse Monte-Carlo method and the blockspin transformation for space directions, we determine 4-dimensional effective monopole action at finite temperature. We get an almost perfect action in the continuum limit under the assumption that the action is composed of two-point interactions alone. It depends on a physical scale $b_s$ and the temperature $T$. The temperature-dependence appears with respect to the spacelike monopole couplings in the deconfinement phase, whereas the timelike monopole couplings do not show any appreciable temperature-dependence. The dimensional reduction of the 4-dimensional SU(2) gluodynamics ((SU(2))$_{4D}$) at high temperature is the 3-dimensional Georgi-Glashow model ($(GG)_{3D}$). The latter is studied at the parameter region obtained from the dimensional red uction. We compare the effective instanton action of $(GG)_{3D}$ with the timelike monopole action obtained from (SU(2))$_{4D}$. We find that both agree very well for $T \ge 2.4T_c$ at large $b$ region. The dimensional reduction works well also for the effective action.Comment: 34 pages, 23 figure

QCD Phase Transition at Finite Temperature in the Dual Ginzburg-Landau Theory

We study the pure-gauge QCD phase transition at finite temperatures in the dual Ginzburg-Landau theory, an effective theory of QCD based on the dual Higgs mechanism. We formulate the effective potential at various temperatures by introducing the quadratic source term, which is a new useful method to obtain the effective potential in the negative-curvature region. Thermal effects reduce the QCD-monopole condensate and bring a first-order deconfinement phase transition. We find a large reduction of the self-interaction among QCD-monopoles and the glueball masses near the critical temperature by considering the temperature dependence of the self-interaction. We also calculate the string tension at finite temperatures.Comment: 13 pages, uses PHYZZX ( 5 figures - available on request from [email protected]