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

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[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