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所有四种力的最有希望的候选者。据推测，所有一致的弦理论都可以从称为 M 理论的单一理论导出。众所周知，M理论存在很多理论挑战，例如量子化。在这项研究中，我阐明了 M 理论的一些方面。它可以分为（1）洛伦兹对称性恢复的检验（2）开膜作为矩阵模型的量子化（3）从M理论角度解释弦结（4）非交换时空的扩展通常通过开弦到开膜情况的边界来定义。在（1）中，我们只进行了经典计算，未来需要量化微积分。在(4)中，它给出了体积守恒微分同胚的量子表示，这与数学物理的许多分支有关。由弦理论定义的时空几何与普通黎曼几何有很大不同在爱因斯坦引力中。在某些限制下，已知几何被简化为Connes 提出的非交换几何。一旦时空变得不可交换，就会出现一种新的孤子配置，这种配置在交换理论中是没有出现的。在这项研究中，我提出这种孤子电荷可以被解释为 C 代数的 K 同调。通过应用这个建议，我考虑了在非交换圆环上定义的孤子配置，并指出出现了一种奇怪的激励，这在现阶段很难在物理上理解。如果开弦定义在这样一个非交换空间上，我们需要引入矩阵弦理论。我们为这样的理论奠定了基础。