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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.

超弦理论是粒子物理学中包括引力在内的统一理论的候选者，在这个理论中我们可以在同一基础上研究时空和物质。基于超弦理论非微扰定义的矩阵模型，我们研究了时空结构及其物质实现。本次资助期间我们取得的主要成果概括为以下三点： 1．我们研究了矩阵模型中的时空结构与超引力理论中的时空结构之间的关系。通过研究矩阵模型中的威尔逊环算子，我们系统地构造了改变超重力理论中背景场配置的各种顶点算子。然后，利用这些顶点算子，分析了超引力多重态对应的场（如引力场）在矩阵模型中的凝聚。 2．我们研究了矩阵模型和非交换几何中物质的手性结构。通过应用格场理论中发展起来的Ginsparg-Wilson关系，我们给出了定义GW狄拉克算子以及制定一般非交换几何中的拓扑不变量和指数的一般规定。我们构造了拓扑非平凡构型，分析了它们的动力学，并加深了对超弦理论和矩阵模型中手性费米子在我们时空中的实现机制的理解。 3．我们发现黑洞的霍金辐射可以用场论中的异常来理解，我们也将其应用于各种黑洞，例如旋转黑洞和高维黑洞。这些结果有望应用于黑洞熵等各种热力学量的研究。