Nonperturbative study of super string theory by matrix models

矩阵模型对超弦理论的非微扰研究

基本信息

批准号：
10044061
负责人：
YONEYA Tamiaki
金额：
$ 1.73万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B).
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10044061/
关键词：
Quantum Gravity Superstring theory Quantum field theory super symmetry unified theory gravitation general relativity black hole

项目摘要

(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

（1）时空不确定性原理：十多年前，Yoneya提出了一种简单的不确定性关系，这限制了时空中最短的可观察距离尺度，因为定性表征了弦乐理论中量子引力的分辨率的定性表征：在本项目中，Yoneya进一步阐明了这一原则。字符串理论的特征长度尺度，特别是M理论量表的作用にないないないないないないないない。（2）D-Branes：我们研究了D-Branes动力学的各种不同方面，这些方面是非驾驶弦线/M理论的关键特征之一。 Kato根据配置电流的自动形态提供了弯曲的时空中的D-Branes公式和Studiod T-对。卡萨马（Kazama）构建了一种一般的路径综合形式，用于研究d-bran…更多的ES和字符串的相互作用。 Jevicki和Yoneya，后来Jevicki，Kazama和Yoneya研究了D-BRANES（广义）形式对称性的角色。我们表明，来自超对称性的约束结合结合的广义结构对称性对于提取eikonal近似中的D型晶体的动力学很有用。 Yoneya研究了D粒子的多体相互作用，并表明超对称性Yang-Mills矩阵量子机制精确地重现了11个维度中超级强度所描述的第一个非线性效应。 Yoneya在矩阵理论中分析了ADS/CFT对应关系的有效性的条件，并获得了相关函数在大N极限中的第一个结果，该函数暴露了一些有趣的行为，这表明筛选机制可能会和解矩阵理论的全息行为与Lorentz不变性。卡萨马（Kazama）扩展了Jevicki，Kazama和Yoneya的先前作品，即通过考虑到超对称性，而无需使Eikonal近似化，并成功地得出了超对称病房的身份，从而更准确地考虑了超对称性，从而扩展了普遍的共形对称性在D-Branes动力学中的作用。 Yoneya在研究具有不稳定D-Branes的系统的对称结构时，表明此类系统在赞助的相位中具有n = 2个时空超对称性。这些最新的作品应该对弦理论的对称结构进行新的启示，并希望成为进一步开发我们计划朝着该理论的非扰动公式发展的有用基础。（3）非交通性结构：卡托从非交通性几何学的角度研究了弦理论中的时空和自由度的结构。尤其是，通过使用完整的非交通性结构构建边界状态，阐明了世界上的非共同量与目标时空的二元性关系，该关系描述了字符串与D-Brane的相互作用。同样，它正在研究背景B场的非交通性的机理中出现在非本地点粒子理论中，该理论的等效性与开放式弦理论的等效性之前显示为以前。最终，关于非交通性结构的研究有望与Yoneya的时空不确定性原理有关。 Yoneya最近在这样的方向上进行的投资表明，确实如此。较少的