Research of Dynamics in Superstring Theories and Field Theories

点击翻译按钮获取中文摘要

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.