Nonperturbative Study of Quantum Gravity and String Theories

超弦理论是自然界四种基本相互作用（强、弱、电磁力和引力）的统一理论中最有希望的候选者之一。通过完善超弦理论来研究基本粒子的性质和宇宙的诞生是最有趣的问题之一。近年来在非摄动构造方面有了很大的发展。其中一个关于“D膜”的公式，即孤子激发和对偶方法变得很重要，然后一种称为M理论的主理论得到了深入的研究。然而，这些非摄动弦理论并没有描述创造和湮灭，因此它们还没有达到第二量子化弦场论。然后，我一直在与丹麦尼尔斯·玻尔研究所的霍尔格·b·尼尔森教授合作，通过使用左右移动模式作为组成部分来构建弦场理论。在这种方法中，我们显然需要一种类似于玻色子粒子中的玻色统计的新的对称性。利用这种对称状态形成。我们现在正在努力推导散射振幅，并检查对偶性是否成立。在研究弦场理论的过程中，我们发现了如何构造玻色子粒子的负能量海（狄拉克海）的方法，使玻色子在二次量子化时可以像对待费米子那样对待玻色子。我们的理论可以解决量子场论中存在已久的玻色子的负能态问题。在量子引力中，我们利用重正化群和统计场理论考虑了2+ε维理论中的近二维引力。通过对其短距离行为的详细研究，得到了标度定律和临界指数。

The superstring theory is one of the most promising candidates for unified theory of the 4 kind of the fundamental interactions in Nature : strong force, weak force, electromagnetic force and gravitational force. It is one of the most interesting problems to investigate the properties of elementary particles and the birth of the universe by completing the superstring theory. Recently there has been a lot of development to construct it nonperturbatively. Among those a formulation in terms of "D brane" which is solitonic excitation and the duality method become important and then a kind of the master theory called M theory has been intensively investigated.However these nonperturbative string theories do not describe creation and annihilation and thus they have not yet come to 2nd quantized string field theory. Then I have been working, with Professor Holger B.Nielsen, the Niels Bohr Institute, Denmark, on constructing string field theory by using the right- and left- moving modes as constituents. In this approach it becomes apparent that we need a new symmetry analogous to the Bose statistics in bosonic particles. By using this symmetry states are formed. We are now working to derive the scattering amplitudes and check whether the duality holds.During the course of studying our string field theory we found the method how to construct the negative energy sea (Dirac sea) for bosonic particles which enables to treat the bosons similar to fermions when second quantizing. Our theory may give a solution to the long standing problem of negative energy states in bosons in quantum field theory.In quantum gravity we considered the gravity in the 2+εdimensional theory near two dimensions by means of the renormalization group and statistical field theory. By studying short distance behavior in detail we obtained scaling law and critical exponents.