Studies in Matrix Model and Spacetime Structure

矩阵模型与时空结构研究

基本信息

批准号：
15540294
负责人：
AOKI Hajime
金额：
$ 2.24万
依托单位：
Saga University (2005-2006)High Energy Accelerator Research Organization (2004)The High Energy Accelerator Research Organization (2003)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2006
项目状态：
已结题

项目摘要

Superstring theory is a candidate for the unified theory including gravity in particle physics, the theory where we can study spacetime and matter at the same footing. Based on the matrix models which are a nonperturbative definition of superstring theory, we study the spacetime structure and the matter realization on it. The main results that we have obtained during the term of this grant are summarized in the following three categories.1. We studied the relation between the spacetime structure in the matrix model and that in the supergravity theory. By investigating the Wilson loop operator in the matrix model, we constructed systematically various vertex operators that alter the background field configurations in the supergravity theory. Then, by using these vertex operators, we analyzed the condensation of the fields corresponding to the supergravity multiplets, such as the gravitational field, in the matrix model.2. We studied the chiral structure of matter in matrix model and noncommutative geometry. By applying the Ginsparg-Wilson relation developed in the lattice field theory, we gave the general prescription to define the GW Dirac operator and to formulate the topological invariant and the index in general noncommutative geometries. We constructed topologically nontrivial configurations, analyzed their dynamics, and developed the understanding of the realization mechanism of chiral fermion on our spacetime in superstring theory and matrix model.3. We found that the Hawking radiation from the black holes can be understood by using the anomaly in the field theory, which we also applied to various black holes, such as the rotating black holes and the higher dimensional black holes. These results are expected to be applied to the study of various thermodynamical quantities such as black hole entropy.

SuperString理论是统一理论的候选者，包括粒子物理学的重力，该理论我们可以在同一基础上研究时空和物质。基于矩阵模型，该模型是对超弦理论的非扰动定义，我们研究了时空结构及其在其上实现的物质。在以下三类中总结了我们在本赠款期间获得的主要结果。1。我们研究了矩阵模型中的时空结构与超级实力理论之间的关系。通过调查矩阵模型中的威尔逊循环操作员，我们系统地构建了各种顶点操作员，以改变超级实力理论中的背景字段配置。然后，通过使用这些顶点运算符，我们分析了矩阵模型中对应于超级重量多重组（例如重力场）的磁场的缩合。2。我们研究了基质模型和非交通性几何形状中物质的手性结构。通过应用晶格场理论中开发的金斯帕格 - 威尔逊关系，我们给出了一般的处方来定义GW Dirac运算符，并在一般的非交易几何形状中制定了拓扑不变性和索引。我们构建了拓扑非平凡的配置，分析了它们的动力学，并在超弦理论和矩阵模型中对手性费物的实现机制的理解发展了3。我们发现，可以通过在田间理论中使用异常来理解来自黑洞的鹰辐射，我们还将其应用于各种黑洞，例如旋转的黑洞和较高的黑色孔。预计这些结果将应用于对各种热力学量（例如黑洞熵）的研究。