TITLE:

Color Confinement, Quark Pair Creation and Dynamical Chiral-Symmetry Breaki\
ng in the Dual Ginzburg-Landau Theory.

ABSTRACT:

We study the color confinement, the $q$-$\bar q$ pair creation and the 
dynamical chiral-symmetry breaking of nonperturbative QCD by using the 
dual Ginzburg-Landau theory, where the dual Higgs mechanism plays an 
essential role on the nonperturbative dynamics in the infrared region. 
As a result of the dual Meissner effect, the linear static quark potential, 
which characterizes the quark confinement, is obtained in the long distance 
within the quenched approximation. We obtain a simple expression for the 
string tension similar to the energy per unit length of a vortex in the 
superconductivity physics. The dynamical effect of light quarks on the 
quark confining potential is investigated in terms of the infrared screening 
effect due to the $q$-$\bar q$ pair creation or the cut of the hadronic 
string. The screening length of the potential is estimated by using the 
Schwinger formula for the $q$-$\bar q$ pair creation. We introduce the 
corresponding infrared cutoff to the strong long-range correlation factor 
in the gluon propagator as a dynamical effect of light quarks, and obtain 
a compact formula for the quark potential including the screening effect 
in the infrared region. We investigate the dynamical chiral-symmetry breaking 
by using the Schwinger-Dyson equation in the dual Ginzburg-Landau theory, 
where the gluon propagator includes the nonperturbative effect related to 
the color confinement. We find a large enhancement of the chiral-symmetry 
breaking by the dual Higgs mechanism, which supports the close relation 
between the color confinement and the chiral-symmetry breaking. 
The dynamical quark mass, the pion decay constant and the quark condensate 
are well reproduced by using the consistent values of the gauge coupling 
constant and the QCD scale parameter with the perturbative QCD and the 
quark confining potential. The light-quark confinement is also roughly 
examined in terms of the disappearance of physical poles in the light-quark 
propagator by using the smooth extrapolation of the quark mass function 
to the time-like momentum region. 

TITLE:

Magnetic Monopole Condensation for Confinement and Chiral 
Symmetry Breaking.

ABSTRACT:

Nonperturbative feature of QCD are investigated using the dual Ginzburg-
Landau theory. The quark confinement is realized through the dual Meissner
effect, when QCD monopoles are condensed. The chiral symmetry is dynamically
broken due to a large contribution of QCD-monopole condensation.

TITLE:

Dual Ginzburg-Landau Theory with QCD Monopoles 
for Dynamical Chiral-Symmetry Breaking.

ABSTRACT:

We study dynamical chiral-symmetry breaking of non-perturbative QCD 
in the dual Ginzburg-Landau theory, where the QCD-monopole field is 
introduced as an essential field for color confinement stemming from 
the choice of the abelian gauge fixing {\it a la} 't Hooft. 
In this theory, QCD-monopole condensation causes the dual Meissner 
effect, which changes the gluon propagator. The dynamical chiral-symmetry
breaking is investigated using the Schwinger-Dyson equation with the
modified gluon propagator in the QCD-monopole condensed vacuum. 
We introduce the low momentum cutoff on the modified gluon propagator 
by considering the effects of the $q$-$\bar q$ pair creation and/or
the quarks being confined in hadrons. We find that dynamical chiral-
symmetry breaking is largely enhanced by QCD-monopole condensation, 
which suggests the close relation between the color confinement and the 
chiral symmetry breaking. The dynamical quark mass, the pion decay constant 
and the quark condensate are reproduced consistently with the confining 
mechanism in this theory. 

TITLE:

Dual Higgs Mechanism for Quarks in Hadrons.

ABSTRACT:

We study nonperturbative features of QCD using the dual Ginzburg-Landau 
(DGL) theory, where the color confinement is realized through the dual 
Higgs mechanism brought by QCD-monopole condensation.
The linear confinement potential appears in the QCD-monopole condensed 
vacuum. We study the infrared screening effect to the confinement potential
by the light-quark pair creation, and derive a compact formula for the 
screened quark potential. We study the dynamical chiral-symmetry breaking 
(D$\chi $SB) in the DGL theory by solving the Schwinger-Dyson equation.
QCD-monopole condensation plays an essential role to D$\chi $SB.
The QCD phase transition at finite temperature is studied using the 
effective potential formalism in the DGL theory. We find the reduction 
of QCD-monopole condensation and the string tension at high temperatures.
The surface tension is calculated using the effective potential at the 
critical temperature. The DGL theory predicts a large mass reduction of
glueballs near the critical temperature. We apply the DGL theory to the 
quark-gluon-plasma (QGP) physics in the ultrarelativistic heavy-ion collisions.
We propose a new scenario of the QGP formation via the annihilation of 
color-electric flux tubes based on the attractive force between them.

TITLE:

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

ABSTRACT:

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.

TITLE:

Distribution of Instanton and Monopole Clustering.

ABSTRACT:

We study the relation between the instanton distribution and the monopole
loop length in the SU(2) gauge theory with the abelian gauge fixing. We
measure the monopole current from the multi-instanton ensemble on the $16^4$
lattice using the maximally abelian gauge. When the instanton density is
dilute, there appear only small monopole loops. On the other hand, in the
dense case, there appears one very long monopole loop, which is responsible
for the confinement property, in each gauge configuration. We find a clear
monopole clustering in the histogram of the monopole loop length from 240
gauge configurations.

TITLE:

Distribution of Instanton and Monopole Clustering.

ABSTRACT:

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.

TITLE:

Chiral Symmetry Breaking in the Dual Ginzburg-Landau Theory.

ABSTRACT:

Confinement and chiral symmetry breaking are the most fundamental phenomena
in Quark Nuclear Physics, where hadrons and nuclei are described in terms of
quarks and gluons. The dual Ginzburg-Landau (DGL) theory, which contains
monopole fields as the most essential degrees of freedom and their
condensation in the vacuum, is modeled to describe quark confinement in
strong connection with QCD. We then demonstrate that the DGL theory is able
to describe the spontaneous break down of the chiral symmetry.

TITLE:

Monopole Dominance for Nonperturbative QCD.

ABSTRACT:

Monopole dominance for the nonperturbative features in QCD is studied both
in the continuum and the lattice gauge theories. First, we study the
dynamical chiral-symmetry breaking (D$\chi $SB) in the dual Higgs theory
using the effective potential formalism. We find that the main driving force
for D$\chi $SB is brought from the confinement part in the nonperturbative
gluon propagator rather than the short-range part, which means monopole
dominance for D$\chi $SB. Second, the correlation between instantons and
QCD-monopoles is studied. In the Polyakov-like gauge, where $A_4(x)$ is
diagonalized, the QCD-monopole trajectory penetrates the center of each
instanton, and becomes complicated in the multi-instanton system. Finally,
using the SU(2) lattice gauge theory with $16^4$ and $16^3 \times 4$, the
instanton number is measured in the singular (monopole-dominating) and
regular (photon-dominating) sectors, respectively. Instantons and anti-
instantons only exist in the monopole sector both in the maximally abelian
gauge and in the Polyakov gauge, which means monopole dominance for the
topological charge.

TITLE:

Clustering of Monopoles in the Instanton Vacuum.

ABSTRACT:

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.

TITLE:

Existence of Chiral-Asymmetric Zero Modes in the Background of QCD-Monopoles

ABSTRACT:

We study topological aspects of the QCD vacuum structure in SU(2) lattice gauge
theory with the abelian ague fixing. The index of the Dirac operator is 
measured by using the Wilson fermion in the quenched approximation. 
We find chiral-asymmetric zero modes in background fields dominated by 
QCD-monopoles without any cooling.

TITLE:

Confinemnet Properties in the Multi-Instanton System

ABSTRACT:

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 $(N/V)^{1 \over 4}$ =200MeV. Thus, instantons directly
relate to color confinement properties.

TITLE:

Confinement Mechanism and Chiral Phase Transition in the Nonperturbative 
vacuum of QCD. 

ABSTRACT:

We study the relation between color confinement and
chiral symmetry breaking in the background of condensed monopoles
at $T=0$ and $T\neq0$.
We formulate the Schwinger-Dyson (SD) equation including the 
vacuum polarization effect, which could remove the infrared singularity, 
in the dual Ginzburg-Landau theory.
In order to solve the SD equation at $T\neq0$, we provide a 
new ansatz for the quark mass function in the imaginary-time formalism.
We find the existence of a strong correlation between the critical temperature
$T_{c}$ of the chiral symmetry restoration and the confinement 
quantity such as the string tension.

TITLE:

Lattice Study of ${\rm U_{A}}(1)$ Anomaly: The Role of QCD-Monopoles.

ABSTRACT:

We investigate the role of QCD-monopoles for the ${\rm U}_{\rm A}(1)$ 
anomaly in the maximally abelian gauge within the SU(2) lattice gauge theory.
The existence of the strong correlation between instantons and QCD-monopoles 
in the abelian gauge was already shown by both analytic and numerical works 
including the Monte Carlo simulation.
Their interrelation brings us a conjecture that the presence of QCD-monopoles 
plays a considerable role on the ${\rm U}_{\rm A}(1)$ anomaly. We find an 
evidence for our conjecture on a determination of the fermionic zero modes 
of the Dirac operator in both the ``monopole removed'' gauge configuration 
and the ``photon removed'' gauge configuration.

TITLE:

Topological Aspect of Abelian Projected SU(2) Lattice Gauge Theory.

ABSTRACT:

We show that the hypothesis of abelian dominance allows QCD-monopoles to 
preserve the topological feature of the QCD vacuum within SU(2) lattice 
gauge theory. An analytical study is made to find the relationship between 
the topological charge and QCD-monopoles in the lattice formulation. 
The topological charge is explicitly represented in terms of the monopole 
current and the abelian component of gauge fields in the abelian dominated 
system. We numerically examine the relation and demonstrate the abelian 
dominance in the topological structure by using Monte Carlo simulation.  

TITLE:

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

ABSTRACT:

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.