Research of Dynamics in Superstring Theories and Field Theories

小组组长，N。Kawamoto等人的研究，澄清了扭曲超对称模型与拓扑场论量子化之间的关系。特别地，这种扭曲过程被称为Dirac-Kaehler扭曲，并且该公式导致N=D=2和N=D=4扭曲的超级杨-米尔斯理论。该公式被应用于构造超对称格模型，以保持超对称性。为了保持格上差分算子的Leibniz定则，我们引入了非交换性，它等价地表示为一个移位交换子。用这种方法我们成功地构造了N=D=2的BF理论、Wess-Zumino模型、超Yang-Mills模型和N=4，D=3的超Yang-Mills模型。有一种说法认为，我们的公式并不完全满足格点上的扭曲超对称性，但我们认为情况并非如此。石川从理论上解决了在高迁移率量子霍尔系统中发现的各向异性霍尔气体的各种令人困惑的问题，如异常的中性无隙模、周期性外势下异常的稳定相、新的量子霍尔区等。所以，K。石川提出了一种新的散射振幅与粒子的动量和位置有关的公式。同时观测两个变量的实验成为通过与新构造的振幅进行比较来获得物理系统新信息的有用手段。Nakayama研究了超弦理论中出现的非对易空间的性质，构造了模糊二球面上非对易积的一种新表示。R.中山还在模糊四球上构造了非对易场论。

The group leader, N. Kawamoto, cleared up the relation between the twisted super symmetric models and quantization of topological field theories. In particular this twisting procedure is named as Dirac-Kaehler twist, and the formulation led to N=D=2 and N=D=4 twisted super Yang-Mills theories. This formulation is applied to construct super symmetric lattice models to keep super symmetry exactly on a lattice. In order to keep the Leibniz rule of difference operator on the lattice, we have introduced noncommutativity which is equivalently expressed by a shifted commutator. In this way we have successfully constructed N=D=2 BF theory, Wess-Zumino model, super Yang-Mills model, and N=4, D=3 super Yang-Mills model on a lattice. There was a claim that our formulation does not satisfy the twisted super symmetry on the lattice exactly, but we claim that this is not the case.K. Ishikawa solved theoretically the various puzzling problems of the anisotropic Hall gas that were found in high mobility quantum Hall system such as unusual neutral gapless modes, unusual stable phases under the periodic external potential, and new quantum Hall regimes and others. Also, K. Ishikawa has formulated a new scattering amplitudes that have dependence on momenta and positions of the particles. Experiments in which both variables are observed became useful means to obtain new information of the physical system by comparing experiments with newly constructed amplitude.R. Nakayama studied the properties of non-commutative spaces which appear in superstring theory and constructed a new representation for non-commutative product on the fuzzy two-sphere. R. Nakayama also constructed non-commutative field theories on fuzzy four-sphere.