Nonperturbative formulation of superstring theory

超弦理论的非微扰表述

基本信息

批准号：
09640337
负责人：
YONEYA Tamiaki
金额：
$ 1.92万
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 (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640337/
关键词：
Quantum Gravity Superstring theory Quantum field theory super symmetry unified theory gravitation general relativity black hole 一般相対性理論弦理論大統一理論場の量子理論

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-bra … More nes 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：十几年前，Yoneya提出了一种简单的不确定性关系，限制了时空最短可观测距离尺度，作为解决量子引力紫外问题的定性表征。在本项目中，Yoneya 进一步阐明和发展了弦理论的特征长度尺度，特别是 M 理论尺度的作用， (2) D-膜：我们研究了 D-膜动力学的各个不同方面，目前认为这是非微扰弦/M 理论的关键特征之一，Kato 在中给出了 D-膜的表述。弯曲时空并在自同构的基础上研究了 T 对偶性Kazama 构建了一种通用路径积分形式来研究 D-bra nes 和弦的相互作用，后来 Jevicki、Kazama 和 Yoneya 研究了 D 的（广义）共形对称性的作用。我们证明了广义共形对称性与来自超对称性的约束相结合对于提取 eikonal 中 D-膜的动力学非常有用。 Yoneya 研究了 D 粒子的多体相互作用，并表明超对称杨-米尔斯矩阵量子力学精确地再现了超引力在 11 维中描述的第一个非线性效应，并分析了 AdS/ 的有效性条件。矩阵理论中的 CFT 对应，并获得了大 N 极限中相关函数的第一个结果，该结果表现出一些有趣的行为，提出了一种可以将矩阵理论的全息行为与Kazama 扩展了 Jevicki、Kazama 和 Yoneya 先前关于广义共形对称性在 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无需进行转角近似，并成功推导了超对称 Ward 恒等式。在研究不稳定 D 膜系统的对称结构时，Yoneya 证明此类系统在自发破缺相中具有 N=2 时空超对称性。最近的工作应该对弦理论的对称结构有新的认识，并希望成为我们进一步发展该理论的非微扰公式的有用基础。 (3) 非交换结构：加藤研究了时空的结构和度。特别是，通过构造描述弦相互作用的完全非交换性边界态，阐明了世界体积中的非交换性与目标时空非交换性之间的对偶关系。与开弦理论等价的非局域点粒子理论中背景B场的非交换性以何种机制出现也在研究中，最终期待非交换结构的研究。与米亚的时空不确定性原理相关。米亚最近沿着这个方向的研究表明情况确实如此。