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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，米谷提出了一个简单的不确定性关系，它限制了时空中最短的可观测距离尺度，作为弦理论中量子引力紫外线问题解决的定性表征：在本项目中，米谷进一步澄清和发展了这一原理。弦理论的特征长度尺度，特别是M理论尺度的作用，g D 31/3（/）s D 3l D 2s D 2，现在可以在这个原理的基础上得到解释。(2)D膜：我们已经研究了D-膜动力学的各种不同方面，这些方面目前被认为是非微扰弦/M理论的关键特征之一。加藤给出了弯曲时空中D-膜的一个公式，并在守恒流的自同构的基础上研究了T-对偶。Kazama建立了一个研究D-bran相互作用的通用路径积分形式 ...更多信息 es和字符串。Jevicki和Yoneya，以及后来的Jevicki，Kazama和Yoneya研究了D-膜的（广义）共形对称的作用。我们证明了广义共形对称结合超对称的约束对于在程函近似中提取D-膜的动力学是有用的。米谷研究了D粒子的多体相互作用，并证明了超对称杨-米尔斯矩阵量子力学精确地再现了11维超引力所描述的第一个非线性效应。米谷分析了矩阵理论中AdS/CFT对应的有效性条件，并获得了大N极限下相关函数的第一个结果，这些结果表现出一些有趣的行为，提出了一种屏蔽机制，可以调和矩阵理论的全息行为与洛伦兹不变性。Kazama扩展了Jevicki，Kazama和Yoneya以前关于广义共形对称在D-膜动力学中的作用的工作，通过更精确地考虑超对称性而不进行程函近似，并成功地导出了超对称Ward恒等式。在研究具有不稳定D膜的系统的对称结构时，米谷证明了这样的系统在自发破缺相中具有N=2的时空超对称性。这些新近的工作应该能使我们对弦理论的对称结构有新的认识，并有望成为进一步发展我们的非微扰理论计划的有用基础。(3)非交换结构：加藤从非对易几何的观点研究了弦理论中的时空结构和自由度。特别地，通过构造描述弦与D-膜相互作用的完全非对易边界态，阐明了世界体积与目标时空体积的非对易性之间的对偶关系.在非定域点粒子理论中，背景B场的非对易性是以何种机制出现的，这一问题也正在研究之中。最后，非对易结构的研究有望与米谷的时空测不准原理联系起来。米谷最近的调查沿着这样一个方向表明，情况确实如此。少