Quantum Theory of Kaluza-Klein (higher dimensional) Field Theory

*在五维晶格SU(2)中进行了Monte Carlo模拟，并研究了紧化额外维的Yang-Mills理论和标度规律。仿真结果表明，随着紧化半径的减小，围相向弱耦合区扩散，理论有效维数由5维逐渐变为4维。在额外的维度中，规范相互作用的红外吸引力被放大。我们发现，这种力可以在红外范围内将软超对称破缺项从基本尺度上的无政府无序状态中排列起来，从而使改变味道的中性电流以及危险的cp违反相在统一尺度上得到充分抑制。*为了在平凡场理论中实现最大局域性，我们通过微调参数的红外值来最大化理论的紫外截止。我们的结果支持了先前提出的主张，即在不可重整场理论中最大化紫外截止可以使理论具有更强的预测能力。*在最近提出的标准模型的最小扩展中的轻子扇区，其中排列对称S3被假设为弱尺度上的精确风味对称，被重新审视。我们发现具有额外ZN对称性的S3在中微子混合中允许CP违反相。轻子扇区包含六个具有两个独立相的实参数，用来描述带电轻子和中微子的质量以及中微子的混合。该模型的预测在不久的将来可以在实验中得到验证。*在封闭链上解构的额外维度自然具有正多边形的对称性，即二面体对称DN。发现Q2N对称在低能时表现为完整的内部全局风味对称。给出了一个基于奇数N的Q6N的具体预测模型。

* Monte Carlo simulations are performed in a five-dimensional lattice SU(2) Yang-Mills theory with, a compactified extra dimension, and scaling laws are studied. Our simulations indicate that as the compactification radius decreases, the confining phase spreads more and more to the weak coupling regime, and the effective dimension of the theory changes gradually from five to four.* In extra dimensions the infrared attractive force of gauge interactions is amplified. We find that this force can align in the infrared limit the soft-supersymmetry breaking terms out of their anarchical disorder at a fundamental scale, in such a way that flavor-changing neutral currents as well as dangerous CP-violating phases are sufficiently suppressed at the unification scale.* To achieve a maximal locality in a trivial field theory, we maximize the ultraviolet cutoff of the theory by fine tuning the infrared values of the parameters. Our result supports the previously made claim that the maximization of the ultraviolet cutoff in an nonrenormalizable field theory can give the theory more predictive power.* The leptonic sector in a recently proposed minimal extension of the standard model, in which the permutation symmetry S3 is assumed to be an exact flavor symmetry at the weak scale, is revisited. We find that S3 with an additional ZN symmetry allows CP violating phases in the neutrino mixing. The leptonic sector contains six real parameters with two independent phases to describe charged lepton and neutrino masses and the neutrino mixing. The predictions of the model can be tested in experiments in near future.* Extra dimension deconstructed on a closed chain has naturally the symmetry of a regular polygon, the dihedral symmetry DN. It is found that the Q2N symmetry appears as an intact, internal global flavor symmetry at low energies. A concrete predictive model based on Q6N with an odd N is given.