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Soliton dynamics and dualities in superstring theory

超弦理论中的孤子动力学和对偶性

基本信息

批准号：
09640352
负责人：
MATSUO Yutaka
金额：
$ 1.73万
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 2000
项目状态：
已结题

项目摘要

String theory is regarded as the most promising candidate to unify all the four forces of the nature. It has been conjectured that all consistent string theory can be derived from a single theory that is called M-theory. It is known that M-theory has a lot of theoretical challenges such as the quantization. In this research, I clarified some aspects of M-theory. It may be classified as (1) examination of the restoration of Lorentz symmetry (2) Quantization of the open membrane as the matrix model (3) Interpretation of string junction from M-theoretical viewpoint (4) extension of the noncommutative space-time which is usually defined through the boundary of the open string to the open membrane situation. In (1), we have carried out only the classical computation and quantized calculus is desirable in the future. In (4), it gives a quantum representation of the volume preserving diffeomorphism, which is related to the many branches of the mathematical physics.The space-time geometry, which is defined by the string theory, is critically different from the ordinary Riemannian geometry in Einstein gravity. In some limit, it is known that the geometry is simplified to the noncommutative geometry that Connes proposed. Once the space-time becomes noncommutative, there appears a new kind of Soliton configuration, which does not appear in the commutative theory. In this research, I proposed that such Soliton charges might be interpreted as the K-homology of the C-algebra. By applying this proposal, I considered the Soliton configuration defined on the noncommutative torus and indicated that there appears a strange excitation, which is difficult to understand physically at this stage. If open string is defined on such a noncommutative space, we need to introduce the matrix string theory. We give a foundation to such a theory.

弦理论被认为是统一自然界中所有四种力的最有希望的候选者。所有相容的弦理论都可以从一个叫做M理论的理论推导出来。众所周知，M理论有很多理论上的挑战，比如量子化。在这项研究中，我澄清了M理论的一些方面。它可以分类为（1）洛伦兹对称性恢复的检验（2）开放膜作为矩阵模型的量子化（3）从M理论观点解释弦结（4）非对易时空的扩展，通常定义为通过边界的开放弦到开放膜的情况。在（1）中，我们只进行了经典计算，量子化微积分是未来的理想。在（4）中，给出了与数学物理的许多分支有关的保体积超纯的量子表示，由弦论定义的时空几何与爱因斯坦引力中的普通黎曼几何有着本质的区别。在一定的限制下，我们知道几何被简化为Connes提出的非对易几何。一旦时空成为非对易的，就会出现一种新的孤子构形，这种构形在对易理论中是不存在的。在本研究中，我提出了这样的孤子荷可以解释为C-代数的K-同调。通过应用这个提议，我考虑了定义在非对易环面上的孤立子配置，并指出出现了一种奇怪的激发，这在现阶段很难物理理解。如果开弦定义在这样的非对易空间上，我们就需要引入矩阵弦理论。我们给这样一个理论的基础。