Emergence of integrability in reduced matrix model and string theory

我们在超对称规范理论的非微扰效应、弦论和量子场论的可积性的融合以及矩阵模型等方面取得了重要进展：i）Itoyama与Kihara和Yoshioka一起计算了所有经典群的四超荷约化矩阵模型的配分函数; ii）Itoyama和Oota在均匀光锥规范中对AdS 5XS 5超弦进行了量子化。（3）与丸吉一起，在FIS（Fujiwara-Sakaguchi-Itoyama）模型中进行了基于Konishi反常的Schwinger-Dyson方程的图解分析和推导。我们证明了Dijkgraaf-Vafa关系对胶子凝聚有效超势的破坏。iv）我们利用S-D方程和Riemann曲面的结构导出了一个精确的关系，它取代了Dijkgraaf-Vafa关系。v）在自发和部分破缺的N=2超对称的研究中，我们成功地将FIS模型扩展到包括了超规范。fields.vi我们构造了N点胶子振幅的近似解，完成了两篇论文。将欧氏空间中的拉普拉斯方程推广到ADS空间中，并构造了相应的解.我们引入了边界环的概念，并论证了它与极小曲面的相关性。problem.vi我们注意到，对于最小面积和BDS胶子振幅，圆的精确解的无穷小变形都是可计算的。vii）Itoyama与Oota和Yoshioka一起在均匀光锥规范中构造了Nambu-Goto型作用量。

We have made significant progress in 1) nonperturbative effects in supersymmetric gauge theory 2) mergence of integrability in string theory and quantum field theory and 3) matrix models.i) With Kihara and Yoshioka, Itoyama evaluated partition function of reduced matrix models with four supercharges for all classical groups.ii) Itoyama and Oota carried out quantization of AdS5XS5 superstrings in the uniform light-cone gauge. Noncommutativity has appeared in the coordinates through Dirac bracket.iii) With Maruyoshi, Itoyama carried out a diagrammatic analysis and the derivation of Schwinger-Dyson equation based on Konishi anomaly in the so-called FIS (Fujiwara-Sakaguchi-Itoyama) model. We showed the violation of the Dijkgraaf-Vafa relation for the gluino condensate effective superpotential.iv) We went ahead to derive an exact relation which replaces the Dijkgraaf-Vafa relation by means of S-D equation and structure of Riemann surfaces.v) In the study of spontaneously and partially broken N=2 supersymmetry, we succeeded in extending the FIS model to include quiver gauge fields.vi) With Mironov and Morozov, Itoyama considered the Alday-Maldacena duality and AdS minimal surfaces. We constructed approximate solutions to N point gluon amplitudes and completed two papers. We derived an extension of Laplace equation in Euclidean space to that in ADS space and constructed the solutions. We introduced the notion of boundary ring and argued its relevance to the minimal surface problem.vi) We continued our investigation. We noticed that infinitesimal deformations to an exact solution to the circle are computable both for the minimal area and for BDS gluon amplitudes. We showed discrepancies of a few coefficients among infinitely many ones, which we regard as an anomaly.vii) With Oota and Yoshioka, Itoyama constructed the Nambu-Goto type action in the uniform light-cone gauge.