String Theory, Matrix Models and Noncommutative Geometry

弦理论、矩阵模型和非交换几何

基本信息

批准号：
13640308
负责人：
ISHIBASHI Nobuyuki
金额：
$ 1.86万
依托单位：
University of Tsukuba (2002-2004)The High Energy Accelerator Research Organization (2001)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640308/
关键词：
String theory D-brane Membrane theory M theory Noncritical Strings Two dimensional quantum gravity Nonperturbative effects String field theory 行列模型 D-instanton D-ブレーン超弦理論ブレーン膜

项目摘要

Superstring theory has been actively studied as a candidate for the unified theory of all the fundamental interactions including gravity. However, the fundamental formulation of the theory is not so well established. The perturbation theory is understood fairly well, but the construction of the field theory of strings is far from being completed. Because of this, we do not understand the fundamental symmetry of the theory and it is difficult to construct the model of elementary particles using this theory. As a fundamental formulation of string theory, matrix models are string theory which are not obvious when we consider the theory as a theory of strings. In this research, we studied the matrix models from the following points of view.Firstly we studied the membrane theory. The strong coupling limit of Type IIA string theory is considered to be described by a theory called M-theory. M-theory can be described as a theory of membranes. Recently, it is proposed that the membrane theory can be described as a matrix quantum mechanics. In this research we studied the matrix quantum mechanics and discuss the worldvolume symmetry of the membranes.Another topic we studied is the noncritical string theory. Noncritical string theory is a string theory in a spacetime with dimension less than 1.Such a string theory can be exactly solved by matrix model approach. It is used as a toy model for the critical ones, especially useful in studying the nonperturbative aspects of string theory. The nonperturbative effects in noncritical string theory are regarded as due to D-instantons. In this research we calculated the chemical potential of these instantons and showed that its value is a universal quantity independent of the method of regularization.

SuperString理论已被积极地作为所有基本相互作用在内的统一理论（包括重力）的候选者。但是，该理论的基本表述并不是很好。扰动理论的理解相当好，但是字段理论的构建远非完成。因此，我们不了解该理论的基本对称性，很难使用该理论构建基本粒子的模型。作为字符串理论的基本表述，矩阵模型是弦理论，当我们将理论视为弦理论时，这并不明显。在这项研究中，我们从以下观点研究了矩阵模型。首先，我们研究了膜理论。 IIA型字符串理论的强耦合极限被认为是一种称为M理论的理论。 M理论可以描述为一种膜理论。最近，有人提出膜理论可以描述为基质量子力学。在这项研究中，我们研究了基质量子力学，并讨论了膜的世界情报对称性。我们研究的另一个主题是非临界弦理论。非临界字符串理论是一个尺寸小于1的时空中的弦理论，可以通过矩阵模型方法来精确地解决字符串理论。它被用作关键的玩具模型，对于研究字符串理论的非扰动方面特别有用。非临界弦理论中的非扰动效应被认为是由于D-Instantons造成的。在这项研究中，我们计算了这些激体子的化学潜力，并表明其值是普遍数量的通用量，而不是正则化方法。