Study of non-perturbative effects of gauge theories using numerical methods

Suzuki等人观察到了颜色限制的阿贝尔机制。在SU(2)流体动力学中以一种规范无关的方式。采用了一种新的随机规范变换降噪方法和多电平方法。从阿贝尔波利亚科夫环相关器得到的静态势给出了正确的弦张力。此外，只有阿贝尔波利亚科夫环中的单极部分负责弦的张力。定义在任意颜色方向上的阿贝尔电场被压缩，相应的单极电流起到磁超电流的作用。穿透长度和相干长度与阿贝尔投影后的观测结果一致。由于所有颜色通道中的阿贝尔中性态都被限制为单重态，因此SU(2)流体动力学中的非阿贝尔色限制可以理解为单粒子引起的阿贝尔对偶迈斯纳效应。久保发现，基于非阿贝尔离散群的某种味道对称性可以在低能量下实现。离散的味道对称性可以起源于压缩的额外维度的几何形状。他们的预测可以被未来的实验所验证，如KEK的大型强子对撞机实验和超级B工厂实验。Nakajima和他的合作者在格子Landau规范QCD中使用淬火和非淬火规范组态分析了运行耦合和Kugo-Ojima约束参数。尽管幽灵和胶子修饰函数测得的运行耦合是红外抑制的，但无论费米子作用如何(威尔逊费米子和Kogut-Susskin费米子)，在$q=0.5$GeV附近，运行耦合的最大值为$\α_0\sim 2-2.5$。在淬火模拟中饱和到约0.8的Kugo-Ojima参数$c$与使用Asqtad作用产生的MILC配置中的期望值1一致。

Abelian mechanism of color confinement is observed bu Suzuki et al. in a gauge-independent way in SU (2) gluodynamics. A new noise-reduction method using random gauge transformations as well as the multi-level method are adopted. A static potential derived from Abelian Polyakov loop correlators gives us the correct string tension. Moreover only the monopole part in the Abelian Polyakov loop is responsible for the string tension. Abelian electric fields defined in an arbitrary color direction are squeezed and the corresponding monopole currents play the role of magnetic super currents. The penetration and the coherence lengths are consistent with those observed previously after Abelian projections. Since an Abelian neutral state in all color channels is restricted to a color-singlet state alone, the non-Abelian color confinement in SU (2) gluodynamics can be understood as the Abelian dual Meissner effect due to monopoles.Kubo found that a certain flavor symmetry based on a non-abelian discrete group can be realized at low energies. Discrete flavor symmetries can originate from the geometry of compactified extra dimensions. They make predictions that can be tested by future experiments such as Large Hadron Colider experiments and Super B-Factory experiments at KEK.The running coupling and the Kugo-Ojima confinement parameter were analyzed by Nakajima and his colaborator in lattice Landau gauge QCD with use of quenched and unquenched gauge configurations. Although the running coupling measured by the ghost and gluon dressing function is infrared suppressed, the running coupling has a maximum of $\alpha_0\sim 2-2.5$ at around $q=0.5$ GeV irrespective of the fermion actions (Wilson fermions and Kogut-Susskind fermions). The Kugo-Ojima Parameter $c$ which saturates to about 0.8 in quenched simulations becomes consistent with the expected value, 1, in the MILC configurations produced with the use of Asqtad action.