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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

[全息重整化群]我们研究了一般时空维度中场论的全息重整化群，并表明当考虑来自弦理论的高阶修正时，系统仍然享有全息原理。我们显式求解了高导数引力理论的Hamilton-Jacobi方程，并证明了在重整化群流中出现了新的多临界点。【全息原理与二维引力中的熵束缚】如何定义二维引力系统的全息原理一直不清楚。指出只要正确地考虑物质场的外尔反常，就能自然地引入这一原理。我们进一步证明了熵界甚至在二维中也存在。[非对易时空和宇宙微波背景]我们通过在infraton场上设置全息截止，在非常早期的宇宙中引入了时空非对易性。我们 ...更多信息指出，这种截止一般抑制角功率谱的宇宙微波背景（CMB）在大角度尺度，这可以解释大尺度阻尼实际上观察到的CMB数据。[循环宇宙]我们证明了，如果我们假设在极早期宇宙中不仅温度而且曲率都存在普朗克能量标度的上界，那么循环宇宙的图像就自然得到了。[非临界弦场论]我们发展了1996年由间和矢彦泽首先给出的非临界弦场论。建立了最小非临界弦理论环振幅和非微扰效应的计算方法。我们进一步建立了弦场论和刘维尔场论中物理观测量之间的对应关系。我们还澄清了圈振幅的代数几何意义。【非临界超弦场论】我们推广了上述非临界弦场论，使其存在世界面超对称性。我们进一步证明了两分量KP族是系统的基本可积结构，这使我们能够解析地计算许多物理量。所得结果与超刘维尔场论的结果完全一致。少