Strong Coupling Gauge Theories and Effective Field Theories

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Along the research plan we have made achievements as follows :( 1 ) We examined a possibility whether or not the top quark condensate can really take place by the Standard Model (SM) gauge dynamics in the extra dimensions, a most recent version of the top quark condensate model, and found that such a theory does have an ultraviolet fixed point and hence the SM gauge coupling does not necessarily yield enough attractive fence to trigger the top quark condensate. We further investigate general feature of the extra dimension gauge theories and found a new phase.( 2 ) The color superconductivity in the finite density phase QCD was investigated through Schwinger-Dyson equation.( 3 ) As to the effective field theories base on the hidden local symmetry (HLS), we found that the chiral symmetry restoration can take place also in the effective field theory for the large number of (massless) flavors in QCD and also pointed out the existence of Seiberg-type duality in non-SUSY QCD. We further proposed "Wilsonian of HLS model, which turned out to yield a very successful phenomenology. This algorithm was then applied for the Large flavor QCD and we found the chiral symmetry restoration would be a such a restoration it was pointed out that the vector dominance is badly violated. It was further shown that the new restoration can also take place in hot and dense QCD, thereby yielding a new basis for the analysis of quark-gluon plasma in RHIC and LHC heavy ion colliders.( 4 ) The DLCQ (Discrete LightCone Quantization) first proposed by Maskawa-Yamawaki (1976) has been an only well-defined framework for the lightcone quantization and hoped to recover the Lorentz invariance in the continuum limit. We demonstrated by explicite computation in the perturbation theory that the Lorentz invarince can never recover although unphysical (measure zero) region of the scattering matrix.