Extended Supersymmetry and Dynamics of Integrable System

本研究项目的目的是阐明场论和弦理论中具有超对称性的可积系统动力学的非微扰性质，其中N大于或等于2。在整个项目期间，我们研究了以下主题。首先，在非线性实现的框架下，阐明了具有超共形对称性或ADS对称性的部分破缺N=2超对称性的各个方面。针对弦理论中的非对易几何，研究了基于Wigner函数和星积的量子化(Uematsu)。给出了N=4超共形代数表示理论的一般而全面的表述，并讨论了包括谱流在内的各个方面。关于可能的额外时空维度，研究了类时间额外维度情况下的物理可观察效应(Matsuda)。第三，The Ca…研究了更多在量子和经典水平上都具有可积多粒子动力学的Logero-Moser系统，揭示了它们的量子可积性的一般结构和它们的对称性(Sasaki)。在弦理论和M理论的背景下，研究了三弦结如何表示为BPS态。本文还研究了场论中de Sitter磁畴壁的实现(Sasakura)。关于B场存在时的非对易几何以及边界弦场理论(BSFT)及其推广也有另一种研究。讨论了作用量与g-函数的关系，构造了脱壳束缚态(Itoyama)。作为本研究小组的一项活动，我们组织了一次关于规范理论和可积模型的研讨会。在目前的研究过程中，与日本国内外相关领域的人士进行讨论和交流是非常有用和不可或缺的。较少

The purpose of the present research project is to clarify the non-perturbative properties of dynamics of the integrable systems in field theory as well as string theory which possess supersymmetry where N is greater than or equal to 2. We have investigated the following subjects throughout the period of the project. First of all, various aspects of the partially broken N = 2 supersymmetry with superconformal or AdS symmetry were clarified in the framework of nonlinear realization. In connection with the noncommutative geometry in string theories, the quantization based on Wigner functions supplemented by the star product was studied (Uematsu). A general and comprehensive formulation of representation theories of N = 4 superconformal algebras was developed and the various aspects including spectral flow were discussed. Concerning the possible extra spacetime dimensions, the physically observable effects in the case of timelike extra dimensions was investigated (Matsuda). Thirdly, the Ca … More logero-Moser systems, which possess integrable multi-particle dynamics at both quantum and classical levels were investaged and the general structure of their quantum integrability as well as their symmetry were revealed (Sasaki). In the context of the string theory and the M-theory, the three-string junction has been studied on how it is represented as a BPS state. The realization of the de Sitter domain wall in field theory was also investigated (Sasakura). There have been another study on the noncommutative geometry in the presence of the B field as well as on the boundary string field theory (BSFT) and its extensions. The relation to the g-function of the action was dicussed and the off-shell bound states were constructed (Itoyama). As an activity of the present research group, we organized a workshop on the gauge theory and integrable models. In the course of the present research, discussions and communications with the people in the related fields inside Japan as well as abroad were very useful and indispensable. Less