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