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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：十多年前，Yoneya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问题解决的定性表征。在本项目中，Yoneya进一步阐明和发展了这一原则。弦理论的特征长度尺度,特别是,m理论的作用,gィイD31/3(/)年代ィエD3lィイD2ィエD2,现在可以解释这一原则的基础上。(2) d -膜：我们研究了d -膜动力学的各种不同方面，d -膜动力学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膜的表述，并在守恒电流自同构的基础上研究了t对偶性。Kazama构造了一个一般的路径积分形式，用于研究D-bra…More nes和string的相互作用。Jevicki和Yoneya，以及后来的Jevicki， Kazama和Yoneya研究了d膜的（广义）共形对称性的作用。我们证明了结合超对称约束的广义共形对称对于在eikonal近似中提取d膜的动力学是有用的。Yoneya研究了d粒子的多体相互作用，并证明了超对称Yang-Mills矩阵量子力学在11维上精确地再现了超引力所描述的第一种非线性效应。Yoneya分析了矩阵理论中AdS/CFT对应的有效性条件，并首次得到了在大N极限下相关函数表现出一些有趣行为的结果，提出了一种将矩阵理论的全息行为与洛伦兹不变性相协调的筛选机制。Kazama扩展了Jevicki， Kazama和Yoneya之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而不做对角逼近，并成功地推导了超对称Ward恒等式。在研究不稳定d膜系统的对称结构时，Yoneya证明了这种系统在一个自发破缺相中具有N=2的时空超对称性。这些最新的研究成果将为弦理论的对称结构提供新的线索，并有望成为进一步发展该理论的非摄动公式的有用基础。(3)非交换结构：Kato从非交换几何的角度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交换性边界态，阐明了世界体积非交换性与目标时空非交换性的对偶关系。此外，本文还研究了背景b场的非定域点粒子理论在与开放弦理论等价的非定域点粒子理论中产生非对易性的机制。最终，非交换结构的研究有望与Yoneya的时空不确定性原理相关。Yoneya最近沿着这个方向进行的调查表明，情况确实如此。少