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中场论的全息重整化群，结果表明，当考虑到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引力理论的Hamilton-Jacobi方程，证明了重整化群流中出现了新的多临界点。我们指出，只要正确考虑物质场的Weyl反常，就可以自然地引入这一原理。[非对易时空与CMB]我们通过在次子场上设置全息截断，在非常早期的宇宙中引入了时空非对易。We…莫尔指出，这种截断通常会抑制宇宙微波背景(CMB)在大角度尺度上的角功率谱，这可以解释在CMB数据中实际观察到的大尺度衰减。[循环宇宙]我们表明，如果我们假设在非常早期的宇宙中不仅存在关于温度的普朗克能量尺度的上限，而且存在关于曲率的上限，那么循环宇宙的图景是自然得到的。[非临界弦场论]我们发展了非临界弦的场论，该理论由Fukuma和Yahikozawa在1996年首次给出。我们建立了最小非临界弦理论的圈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Liouville场论中的物理能观之间的对应关系。我们还阐明了回路振幅的代数几何意义。[非临界超弦场论]我们对上述非临界弦场论进行了推广，使之存在世界板超对称性。我们进一步证明了两分量Kp族是系统的基本可积结构，这使得我们能够解析地计算许多物理量。所得结果与超Liouville场论的结果完全一致。较少

[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