Emergence of Integrability in Gauge Theory and String Theory

2004学年，Itoyama与Fujiwara（研究生）和Sakaguchi（COE博士后研究员）合作，开始了N=2超对称性自发部分破缺的研究，试图找到与Morozov和Kanno合作进行的关于Gluino凝聚预势的研究的新进展，直到2003学年。我们的研究在两篇发表的论文和一份会议记录中进行了总结。人们一直认为，刚性扩展超对称的自发部分破缺是很难实现的。在第一篇论文中，我们成功地构造了一个U（N）规范模型，它摆脱了这个约束，并与大统一理论有关。Fayet-Iliopoulos项的反演和Kahler势所具有的U（N）等距性的度量所必然伴随的离散R不变性起着重要的作用。在第二篇文章中，我们识别了退化真空，并导出了质量公式。 ...更多信息 2005学年，我们进一步推进了2004年的研究。我们成功地在调和超空间中建立了上述模型的明显不变公式，并成功地将模型扩展到包括物质超多重态。我还指导了Maruyoshi关于U（N）规范N=2超引力的部分susy破缺的硕士论文，并编写了预印本。另外，我恢复了对我和Tokura不久前提出的USp矩阵模型的研究。与Yoshioka一起，我们在模型中列举了4个或8个超荷的Z_3轨道折叠的可能性（Phys. RevD）。目前，Kihara，Yoshioka和我正在完成一篇关于USp矩阵模型精确评估的论文，使用摩尔，Nekrasov和Shatashvili的上同调方法。在这项工作的过程中，我们还开发了一种方法的矩阵积分的单根和Weyl群的李代数，我们也准备另一篇论文。少

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