Extended Supersymmetry and Dynamics of Integrable System

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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