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场论的全息重整化群，并表明当考虑来自弦理论的高阶校正时，系统仍然享有全息原理我们明确地解决了 Hamilton-Jacobi 问题。 [全息原理与二维引力中的熵界]目前还不清楚如何定义我们指出，通过正确考虑物质场的韦尔异常，可以自然地引入该原理。我们进一步表明，即使在二维中，熵界也存在。 CMB]我们通过在次子场上设置全息截止，在极早期的宇宙中引入了时空非交换性。我们指出，这种截止通常会抑制角功率谱。大角度尺度的宇宙微波背景（CMB），这可以解释在CMB数据中实际观察到的大尺度阻尼。[循环宇宙]我们证明，如果我们假设存在上限，则自然获得循环宇宙的图像普朗克能量尺度不仅与温度有关，而且与极早期宇宙的曲率有关。[非临界弦场论]我们发展了非临界弦场论，该理论由 Fukuma 和 Yahikozawa 在1996年，我们建立了最小非临界弦理论的环振幅和非微扰效应的计算方法，进一步建立了弦场论中的物理可观测量与刘维尔场论中的物理可观测量之间的对应关系，并阐明了[非临界超弦场论] 我们以存在世界面超对称性的方式扩展了上述非临界弦场论。二元KP层次是系统的底层可积结构，它使我们能够解析计算许多物理量，所得到的结果与超刘维尔场论中得到的结果完全一致。