Emergence of Integrability in Gauge Theory and String Theory

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In 2004 academic year, Itoyama initiated research on spontaneous partial breaking of N=2 supersymmetry, in collaboration with Fujiwara (graduate student) and Sakaguchi (COE postdoctoral fellow), trying to find a new development of the research on the gluino condensate prepotential carried out in collaboration with Morozov and Kanno till 2003 academic year. Our investigation was summarized in the two published papers and one report in the conference proceedings. It had been thought that spontaneous partial breaking of rigid extended supersymmetry is hard to come by. In the first paper, we succeeded in constructing a U(N) gauge model which escapes this constraint and which is related to grand unified theories. The discrete R invariance which is necessarily accompanied with the inversion of the Fayet-Iliopoulos term and the gauging of the U(N) isometry possessed by the Kahler potential play important roles. In the second paper, we identified the degenerate vacua and derived the mass formu … More la which takes a form of the third prepotential derivatives.In 2005 academic year, we pushed the investigation of 2004 further. We succeeded in a manifestly invariant formulation of the above model in harmonic superspace and succeeded in extending a model to include matter hypermultiplets. I also supervised the master thesis of Maruyoshi on partial susy breaking of U(N) gauged N=2 supergravity and a preprint has been written. Separately, I resumed investigation of the USp matrix model proposed some time ago by myself and Tokura. With Yoshioka, we enumerated the possibilities of Z_3 orbifolding with 4 or 8 supercharges within the model (Phys.Rev D). Currently Kihara, Yoshioka and myself are finishing up a paper on the exact evaluation of USp matrix model, using the cohomology method of Moore, Nekrasov and Shatashvili. In the course of this work, we also developed a method of matrix integrations in terms of simple roots and Weyl groups of the Lie algebras, on which we are also preparing another paper. Less