Gluonic Higgs Scalar, Abelianization and Monopoles in QCD -- Similarity and Difference between QCD in the MA Gauge and the NAH Theory

We study the similarity and the difference between QCD in the maximally abelian (MA) gauge and the nonabelian Higgs (NAH) theory by introducing the ``gluonic Higgs scalar field'' $\vec \phi(x)$ corresponding to the ``color-direction'' of the nonabelian gauge connection. The infrared-relevant gluonic mode in QCD can be extracted by the projection along the color-direction $\vec \phi(x)$ like the NAH theory. This projection is manifestly gauge-invariant, and is mathematically equivalent to the ordinary MA projection. Since $\vec \phi(x)$ obeys the adjoint gauge transformation and is diagonalized in the MA gauge, $\vec \phi(x)$ behaves as the Higgs scalar in the NAH theory, and its hedgehog singularity provides the magnetic monopole in the MA gauge like the NAH theory. We observe this direct correspondence between the monopole appearing in the MA gauge and the hedgehog singularity of $\vec \phi(x)$ in lattice QCD, when the gluon field is continuous as in the SU($N_c$) Landau gauge. In spite of several similarities, QCD in the MA gauge largely differs from the NAH theory in the two points: one is infrared monopole condensation, and the other is infrared enhancement of the abelian correlation due to monopole condensation.Comment: Talk given at 16th International Conference on Particles and Nuclei (PANIC 02), Osaka, Japan, 30 Sep - 4 Oct 200

Y-type Flux-Tube Formation and Gluonic Excitations in Baryons: From QCD to Quark Model

Using SU(3) lattice QCD, we perform the first systematic study for the ground-state three-quark (3Q) potential $V_{\rm 3Q}^{\rm g.s.}$ and the 1st excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$, {\it i.e.}, the energies of the ground state and the 1st excited state of the gluon field in the presence of the static three quarks. From the accurate and thorough calculation for more than 300 different patterns of 3Q systems, the static ground-state 3Q potential $V_{\rm 3Q}^{\rm g.s.}$ is found to be well described by the Coulomb plus Y-type linear potential, {\it i.e.}, Y-Ansatz, within 1%-level deviation. As a clear evidence for Y-Ansatz, Y-type flux-tube formation is actually observed on the lattice in maximally-Abelian projected QCD. For more than 100 patterns of 3Q systems, we calculate the 1st excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$ in quenched lattice QCD, and find the gluonic excitation energy $\Delta E_{\rm 3Q} \equiv V_{\rm 3Q}^{\rm e.s.}-V_{\rm 3Q}^{\rm g.s.}$ to be about 1 GeV. This large gluonic-excitation energy is conjectured to ensure the success of the quark model for the low-lying hadrons even without gluonic excitations.Comment: Talk given at International Conference on Color Confinement and Hadrons in Quantum Chromodynamics - Confinement 2003, RIKEN, Japan, 21-24 Jul 200

Chiral Symmetry Breaking in the Dual Ginzburg-Landau Theory

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.Comment: Talk presented by H. Toki at the Joint Japan-Australia Workshop on ``Quarks, Hadrons and Nuclei'', 15 - 24 Nov. 1995, in Adelaide, Australia, 7 pages, Plain Latex, 4 postscript figures (included in a separate .uu file