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

[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，并证明当考虑弦理论的高阶修正时，系统仍然具有全息原理。我们显式地求解了高导数重力理论的Hamilton-Jacobi方程，证明了重整化群流中出现了新的多临界点。[二维引力中的全息原理和熵界]如何定义二维引力系统的全息原理一直不清楚。指出正确地考虑到物质场的Weyl异常，可以很自然地引入这一原理。我们进一步证明了即使在二维空间中熵界也存在。[非对易时空和CMB]我们通过在次元场上设置全息截断，在非常早期的宇宙中引入了时空非对易性。More指出，这种截断在大角度尺度上普遍抑制了宇宙微波背景（CMB）的角功率谱，这可以解释在CMB数据中实际观测到的大尺度阻尼。[循环宇宙]我们证明，如果我们假设在非常早期的宇宙中，不仅在温度上，而且在曲率上都存在一个普朗克能量尺度的上界，那么循环宇宙的图景是自然得到的。[非临界弦场论]我们发展了由Fukuma和Yahikozawa于1996年首次提出的非临界弦场论。建立了最小非临界弦理论的环幅值和非微扰效应的计算方法。进一步建立了弦场论中物理观测值与刘维尔场论中物理观测值的对应关系。我们还阐明了环幅值的代数-几何意义。[非临界超弦场论]我们对上述非临界弦场论进行了扩展，使其存在一个世界表超对称。我们进一步表明，双组分KP层次是系统的潜在可积结构，这使我们能够分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

[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