Strong Coupling Gauge Theories and Effective Field Theories

沿着研究计划，我们取得了以下成果：(1)我们考察了标准模型(SM)规范动力学在额外维度中是否真的可以发生顶夸克凝聚体的可能性，发现这样的理论确实存在紫外线不动点，因此SM规范耦合不一定产生足够吸引的栅栏来触发顶夸克凝聚体。(2)利用Schwinger-Dyson方程研究了有限密度相QCD中的色超导电性。(3)对于基于隐藏局域对称性(HLS)的有效场论，我们发现对于QCD中的大量(无质量)味，手征对称性恢复也可以在有效场论中发生，并指出了非超对称QCD中Seiberg型对偶的存在。我们进一步提出了HLS的威尔逊模型，该模型产生了一个非常成功的现象学。然后将该算法应用于大味道QCD，我们发现手征对称性恢复将是这样的恢复，指出矢量优势被严重破坏。这进一步表明，新的恢复也可以发生在热而密集的QCD中，从而为RHIC和LHC重离子对撞机中的夸克-胶子等离子体的分析提供了新的基础。(4)Maskawa-Yamwaki(1976)首先提出的离散光锥量子化(DLCQ)是唯一定义明确的光锥量子化框架，希望在连续谱极限下恢复洛伦兹不变性。我们用微扰理论中的显式计算证明了洛伦兹逆现象在散射矩阵的非物理(测量为零)区域是不可能恢复的。

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.