1,285 research outputs found

### Abelianization of QCD in the Maximally Abelian Gauge and the Nambu-'t Hooft Picture for Color Confinement

We study the Nambu-'t Hooft picture for color confinement in terms of the
abelianization of QCD and monopole condensation in the maximally abelian (MA)
gauge. In the MA gauge in the Euclidean metric, the off-diagonal gluon
amplitude is strongly suppressed, and then the off-diagonal gluon phase shows
strong randomness, which leads to rapid reduction of the off-diagonal gluon
correlation. In SU(2) and SU(3) lattice QCD in the MA gauge with the abelian
Landau gauge, the Euclidean gluon propagator indicates a large effective mass
of the off-diagonal gluon as $M_{\rm off} \simeq 1 {\rm GeV}$ in the
intermediate distance as $0.2{\rm fm} \le r \le 0.8{\rm fm}$. Due to the
infrared inactiveness of off-diagonal gluons, infrared QCD is well abelianized
like nonabelian Higgs theories in the MA gauge. We investigate the
inter-monopole potential and the dual gluon field $B_\mu$ in the MA gauge, and
find longitudinal magnetic screening with $m_B \simeq$ 0.5 GeV in the infrared
region, which indicates the dual Higgs mechanism by monopole condensation. We
define the ``gluonic Higgs scalar field'' providing the MA projection, and find
the correspondence between its hedgehog singularity and the monopole location
in lattice QCD.Comment: Invited talk given at QCD02: High-Energy Physics International
Conference in Quantum Chromodynamics, Montpellier, France, 2-9 Jul 200

### Instantaneous Interquark Potential in Generalized Landau Gauge in SU(3) Lattice QCD: A Linkage between the Landau and the Coulomb Gauges

We investigate in detail "instantaneous interquark potentials", interesting
gauge-dependent quantities defined from the spatial correlators of the temporal
link-variable $U_4$, in generalized Landau gauge using SU(3) quenched lattice
QCD. The instantaneous Q$\bar{\rm Q}$ potential has no linear part in the
Landau gauge, and it is expressed by the Coulomb plus linear potential in the
Coulomb gauge, where the slope is 2-3 times larger than the physical string
tension. Using the generalized Landau gauge, we find that the instantaneous
potential can be continuously described between the Landau and the Coulomb
gauges, and its linear part rapidly grows in the neighborhood of the Coulomb
gauge. We also investigate the instantaneous 3Q potential in the generalized
Landau gauge, and obtain similar results to the Q$\bar{\rm Q}$ case. $T$-length
terminated Polyakov-line correlators and their corresponding "finite-time
potentials" are also investigated in generalized Landau gauge

### 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 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

### The Role of Monopoles for Color Confinement

We study the role of the monopole for color confinement by using the monopole
current system. For the self-energy of the monopole current less than
ln$(2d-1)$, long and complicated monopole world-lines appear and the Wilson
loop obeys the area law, and therefore the monopole current system almost
reproduces essential features of confinement properties in the long-distance
physics. In the short-distance physics, however, the monopole-current theory
would become nonlocal due to the monopole size effect. This monopole size would
provide a critical scale of QCD in terms of the dual Higgs mechanism.Comment: 3 pages LaTeX, 3 figures, uses espcrc2.sty, Talk presented at
lattice97, Edinburgh, Scotland, July. 199

### 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

### A Remark on the Large Difference between the Glueball Mass and T(C) in Quenched QCD

The lattice QCD studies indicate that the critical temperature $T_c \simeq
260-280$ MeV of the deconfinement phase transition in quenched QCD is
considerably smaller than the lowest-lying glueball mass $m_{\rm G} \simeq
1500-1700$ MeV, i.e., $T_c \ll m_{\rm G}$. As a consequence of this large
difference, the thermal excitation of the glueball in the confinement phase is
strongly suppressed by the statistical factor as $e^{-m_{\rm G}/T_c} \simeq
0.00207$ even near $T \simeq T_c$. We consider its physical implication, and
argue the abnormal feature of the deconfinement phase transition in quenched
QCD from the statistical viewpoint. To appreciate this, we demonstrate a
statistical argument of the QCD phase transition using the recent lattice QCD
data. From the phenomenological relation among $T_c$ and the glueball mass, the
deconfinement transition is found to take place in quenched QCD before a
reasonable amount of glueballs is thermally excited. In this way, quenched QCD
reveals a question ``what is the trigger of the deconfinement phase transition
?''Comment: 6 pages, 4 figure

- …