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

*在五维格子SU(2)Yang-Mills理论中进行了蒙特卡罗模拟，并研究了标度律。我们的模拟表明，随着压缩半径的减小，禁闭相越来越多地向弱耦合区域扩展，理论的有效维度从5维逐渐变化到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使软超对称性破缺项在基本尺度上对齐，从而在统一尺度上充分抑制气味变化的中性电流和危险的CP破坏相。*为了在平凡场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线截止。我们的结果支持了以前的说法，即在不可重正化场理论中最大化紫外线截止可以给理论更好的预测能力。*重新讨论了最近提出的标准模型的最小扩展中的轻子部分，其中排列对称性S3被假设为弱尺度上的精确味道对称性。我们发现，具有附加ZN对称性的S3允许中微子混合中的CP破坏相。轻子扇区包含六个实参数和两个独立的相，用于描述带电的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，即二面体对称性Dn。研究发现，在低能下，Q2N对称性表现为完整的内部整体风味对称性。给出了基于奇数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.