Study of the holographic principle in gravity theory and the constructive definition of string theory

引力理论中的全息原理研究及弦理论的构造性定义

基本信息

批准号：
15540269
负责人：
FUKUMA Masafumi
金额：
$ 2.24万
依托单位：
Kyoto University
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

[Holographic Renormalization Group] We studied the holographic renormalization group for field theories in generic spacetime dimensions, and showed that the systems still enjoy the holographic principle when higher-order corrections coming from string theory are taken into account. We explicitly solved the Hamilton-Jacobi equations of higher-derivative gravity theory, and showed that there appear new multi-critical points in the renormalization group flows.[Holographic principle and entropy bound in two-dimensional gravity] It had not been clear how to define the holographic principle for two-dimensional gravity systems. We pointed out that the principle can be naturally introduced by correctly taking account of the Weyl anomaly of matter fields. We further showed that the entropy bound also exists even in two dimensions.[Noncommutative spacetime and the CMB] We introduced a spacetime noncommutativity in the very early universe by setting a holographic cutoff on the infraton field. We … More pointed out that such cutoff generically suppresses the angular power spectrum of the cosmic microwave background (CMB) at large angular scales, which could explain the large-scale damping actually observed in the CMB data.[Cyclic universe] We showed that the picture of cyclic universe is naturally obtained if we assume that there exists an upper bound of Planck energy scale not only on the temperature but also on the curvature in the very early universe.[Noncritical string field theory] We developed the field theory of noncritical strings which was first given by Fukuma and Yahikozawa in 1996. We established the calculational methods to obtain loop amplitudes and nonperturbative effects of minimal noncritical string theory. We further established the correspondence between the physical observables in the string field theory and those in Liouville field theory. We also clarify the algebraic-geometrical meaning of loop amplitudes.[Noncritical superstring field theory] We extended the above-mentioned noncritical string field theory in such a way that there exits a worldsheet supersymmetry. We further showed that the two-component KP hierarchy is the underlying integrable structure of the system, which enables us to calculate many physical quantities analytically. The obtained results were shown to completely agree with those obtained in super-Liouville field theory. Less

[全息重新归一化组]我们研究了通用时空维度的现场理论的全息重质化组，并表明当考虑到弦理论的高阶校正时，系统仍然享受全息原理。我们明确地解决了更高衍生性重力理论的汉密尔顿 - 雅各比方程，并表明在重新归一化组流中出现了新的多临界点。[全息原理和以二维引力结合的熵]尚不清楚如何清楚如何定义二维重力系统的二维性重态系统。我们指出，通过正确考虑物质领域的Weyl异常，可以自然引入原则。我们进一步表明，即使在两个维度上也存在熵结合。[非交换时空和CMB]，我们通过在Infraton领域设置全息图临界值，在早期的宇宙中引入了时空的非交通生活方式。我们……更多地指出，这种截止的一般抑制了宇宙微波背景（CMB）在大型角度尺度上的角度谱，这可以解释在CMB数据中实际上观察到的大尺度阻尼。[环状宇宙] [环形宇宙]我们还表明，如果我们在comclic的图像上也不是在plans上，那么在plance上也没有范围的范围。早期的宇宙。[非关键弦字段理论]我们开发了非批评弦的领域理论，该理论是福马和Yahikozawa于1996年首次给出的。我们建立了计算方法，以获得循环放大器和最小非临界弦理论的非扰动效应。我们进一步建立了弦场理论中的物理可观察物与liouville田地理论中的对应关系。我们还阐明了循环放大器的代数几何含义。[非批评超弦场理论]我们扩展了上述非批判性弦乐场理论，以使世界上的超对称性退出。我们进一步表明，两个组分的KP层次结构是系统的基本集成结构，这使我们能够分析地计算许多物理量。所获得的结果表明与超洛维尔田间理论中获得的结果完全一致。较少的