Strong Coupling Gauge Theories and Effective Field Theories

根据研究计划，我们取得了以下成果：(1)我们检验了标准模型规范动力学在额外维度是否真的会发生顶夸克凝聚的可能性，这是顶夸克凝聚模型的最新版本，并且发现该理论确实存在紫外线固定点，因此SM规范耦合不一定产生足够的吸引fence来触发顶夸克凝聚。我们进一步研究了额外维度规范理论的一般特征，发现了一个新的阶段。(2)利用Schwinger-Dyson方程研究了有限密度相QCD的彩色超导性。(3)对于基于隐局域对称（HLS）的有效场论，我们发现对于QCD中大量（无质量）味质的有效场论也可以发生手性对称性恢复，并指出了非susy QCD中seiberg型对偶的存在。我们进一步提出了“HLS的威尔逊模型”，这是一个非常成功的现象学。然后将该算法应用于大风味QCD，我们发现手性对称性恢复将是这样的恢复，并指出矢量优势性严重违反。进一步表明，这种新的恢复也可以在高温和致密的QCD中发生，从而为RHIC和LHC重离子对撞机中夸克-胶子等离子体的分析提供了新的基础。(4) Maskawa-Yamawaki（1976）首次提出的离散光锥量化（DLCQ）是光锥量化唯一定义明确的框架，希望在连续体极限下恢复洛伦兹不变性。我们在微扰理论中通过显式计算证明，尽管散射矩阵的非物理（测量零）区域，但洛伦兹不变性永远无法恢复。

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.