Nonperturbative study of super string theory by matrix models

（1）空间时间不确定原则：超过10年前， Yoneya提出了一个简单的不确定关系，限制了空间时间中最短的可观察距离尺度，即字符串理论中量子重力的分辨率的合格特征：目前的项目这一原则由Yoneya进一步界定和开发。字符串理论的字符长度尺度，在粒子中，M-理论尺度的作用，gy D31/3（/）sy D3 ly D2 sy D2，现在可以解释这个原则的基础。（2）D-布兰：我们研究了D-branes动力学的不同方面的变化，他们现在相信成为非持久字符串/M理论的关键特征之一。Kato在曲线空间-时间和受委托的曲线上研究的T-二元性的基础上形成了D-branes的形式。Kazama为研究D-Bran的相互作用构建了一个通用的路径-整体形式主义 ... More E和弦。Jevicki和Yoneya，后来的Jevicki， Kazama和Yoneya研究了D-布兰尼斯的（通用化）一致性对称性。我们展示了从超对称中提取D-branes的动力学在均衡近似中的作用中的通用一致性对称性。Yoneya研究了D粒子的多体相互作用，并展示了超对称性Yang-Mills矩阵量子力学，通过超重力在11个维度中精确地再现了第一个非线性效应。Yoneya分析了矩阵理论中AdS/CFT相关响应的有效性的条件，并获得了较大N限制中相关函数的第一个结果，以展示一些有趣的行为，建议筛选机制，其中可能重新考虑使用Lorentz变量的矩阵理论的全息行为。Jevicki、Kazama和Yoneya在D-branes动力学中的通用一致性对称性的作用下扩展了前一项工作，并将超级对称性描述为更精确地在没有制定电子近似值并成功地产生超级对称性病房身份。在研究带有不稳定D-branes的系统的对称性结构时， Yoneya展示了这样的系统在一个自然中断的阶段有N=2空间-时间超对称性。这些最近的作品应该在字符串理论的对称性结构上投射新的光芒，并希望成为一个有用的基础，以便在我们的程序的进一步发展中实现该理论的非局部公式。（3）非交替结构： Kato从字符串理论的视点对空间时间和自由程度的结构进行了调查。特别是，世界范围内的非通信性之间的双重关系和目标空间时间是由界定的，以构建具有完整的非通信性的边界状态，描述了字符串与D分支的相互作用。此外，它还在研究什么机制下的非可交易性是由背景B场在非地方点粒子理论中出现的，谁的平等性对开放弦理论在之前显露出来。最后，关于非交互式结构的研究似乎与Yoneya的空间-时间不确定原则有关。Yoneya最近的调查对这一方向提出了一项建议，这将证明这一点。Less（低）

(1) Space-time uncertainty principle: More than ten years ago, Yoneya has proposed a simple uncertainty relation, which restricts the shortest observable distance scales in space-time, as a qualitative characterization of the resolution of the ultraviolet problems of quantum gravity in string theory : During the present project this principle was further clarified and developed by Yoneya. The characteristic length scales of string theory, in particular, the role of the M-theory scale, gィイD31/3(/)sィエD3lィイD2sィエD2, can now be explained on the basis of this principle. (2) D-branes : We have investigated a variety of different aspects of the dynamics of D-branes which are presently believed to be one of the key features for the nonperturbative string/M theory. Kato gave a formulation of D-branes in curved space-time and studied T-dualities on the basis of the automorphisms of the conserved currents. Kazama constructed a general path-integral formalism for studying the interactions of D-bran … More es and strings. Jevicki and Yoneya, and later Jevicki, Kazama and Yoneya studied the role of (generalized) conformal symmetries for D-branes. We showed that the generalized conformal symmetry in conjunction of the constraint coming from supersymmetry is useful for extracting the dynamics of D-branes in the eikonal approximation. Yoneya studied the multi-body interactions of D-particles, and showed that the supersymmetry Yang-Mills matrix quantum mechanics precisely reproduces the first nonlinear effect described by the supergravity in 11 dimensions. Yoneya analyzed the condition for the validity of the AdS/CFT correspondence in Matrix theory and obtained the first results for the correlation functions in the large N limit which exhibit some interesting behavior, suggesting a screening mechanism which may reconcile the holographic behavior of the matrix theory with Lorentz invariance. Kazama extended the previous work by Jevicki, Kazama and Yoneya on the role of generalized conformal symmetry in the dynamics of D-branes by taking account the supersymmetry more precisely without making the eikonal approximation and succeeded to derive the supersymmetric Ward identity. In studying the symmetry structure for systems with unstable D-branes, Yoneya showed that such systems have N=2 space-time supersymmetry in a spontaneously broken phase. These more recent works should shed new light on the symmetry structure of string theories and are hoped to be a useful basis for further development of our program toward the nonperturbative formulation of the theory. (3) Noncommutative structure: Kato investigated the structure of spacetime and degrees of freedom in string theory from the viewpoint of noncommutative geometry. Especially, the duality relation between the noncommutativity in the world volume and that of the target spacetime was clarified by constructing the boundary state with full noncommutativity which describes the interaction of string with D-brane. Also it is under study in what mechanism the noncommutativity by the background B-field appears in the non-local point particle theory Whose equivalence to the open string theory was shown before. Ultimately, the studies on noncommutative structure are expected to be related to Yoneya's space-time uncertainty principle. Yoneya's recent investigation along such a direction suggests that will be indeed the case. Less