Emergence of Integrability in Gauge Theory and String Theory

2004学年，Itoyama开始与藤原（研究生）和坂口（COE博士后）合作研究N=2超对称的自发部分破缺，试图在与Morozov和Kanno合作进行的胶子凝聚预势研究中找到新的发展。我们的调查总结在两篇已发表的论文和会议论文集中的一篇报告中。人们一直认为刚性扩展超对称的自发部分破缺是很难得到的。在第一篇论文中，我们成功地构造了一个U(N)规范模型，它摆脱了这一约束，并且与大统一理论有关。离散R不变性必然伴随着Fayet-Iliopoulos项的反演和Kahler势所具有的U(N)等距测量，在此过程中起着重要的作用。在第二篇论文中，我们确定了简并真空，并推导出了质量公式，其形式为三阶前势导数。2005学年，我们进一步推进了2004年的调查工作。我们成功地在调和超空间中得到了上述模型的明显不变公式，并成功地将模型扩展到包含物质超多重态。我还指导了Maruyoshi关于N=2超重力U(N)的部分易破的硕士论文，并写了预印本。另外，我重新研究了前一段时间我和Tokura提出的USp矩阵模型。与Yoshioka一起，我们在模型中列举了4或8个增压时Z_3成轨道的可能性。牧师D)。目前，Kihara， Yoshioka和我正在完成一篇关于USp矩阵模型精确评价的论文，使用Moore， Nekrasov和Shatashvili的上同调方法。在这项工作的过程中，我们还开发了一种基于李代数的单根和Weyl群的矩阵积分方法，我们也在准备另一篇论文。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