Quantum study of ground state and black holes in superstring theories

本研究取得了以下成果：(1)研究弦理论中在膜上实现的非对易理论对于深入理解量子引力具有重要意义。我们不仅研究了空间和空间坐标之间的非对易理论，而且研究了空间和时间之间的非对易理论，为这些理论的非微扰分析奠定了基础。此外，我们还显式地研究了三维理论在对偶条件下的变换性质。我们还研究了在这些理论中实现为孤子解的D膜的超对称性和涨落谱。作为这项工作的推广，我们证明了如果我们有非平凡的背景，D和反D-膜系统中存在连续的超对称性。文中还阐明了孤子的模空间，并将结果用于考察孤子的散射。(2)含时解对于用弦理论研究黑洞的形成和宇宙学具有重要意义。当我们在这样的时空中考虑D-膜时，我们证明了场论和/或开弦理论在膜上实现。我们还给出了最一般的含时膜解。它们是与时间相关的内部空间大小的精确解，事实证明，它们给出了非常有趣的带膨胀的宇宙模型。它们给出了非常有前途的模型来解释当前的加速膨胀的宇宙，并引起了人们的极大关注。(3)PP波时空是弦理论的可解背景，因此是非常有趣的背景。我们研究了这种几何，重点放在解的超对称方面。此外，我们还发展了一种系统的方法来推导各种形式的p-膜((p+1)维)作用量，并计划将结果用于研究p-膜的量子化。

This research project achieved the following results.(1) It is important to study noncommutative theories realized on branes in string theories in order to gain deep understanding of quantum gravity. We have studied theories with noncommutativity not only between space and space coordinates but also space and time, and have given foundation to the nonperturbative analysis of these theories. Furthermore we explicitly examined the transformation properties of 3-dimensional theories under duality. We have also studied supersymmetry and fluctuation spectrum around D-branes realized as solitonic solutions in these theories. As an extention of this work, we showed that there is unbroken supersymmetry in D and anti-D-brane system if we have nontrivial backgrounds. The moduli space of solitons is also clarified and the results are used to examine their scatterings.(2) Time-dependent solutions are important to study formation of black holes and cosmology in terms of string theory. When we consider D-branes in such space-time, we showed that field theories and/or open string theories are realized on the branes. We have also given most general time-dependent brane solutions. They are exact solutions with time-dependent size of the internal space, and it turns out that they give very interesting cosmological models with inflation. They give very promising models to explain the present expanding universe with acceleration and attract much, attention.(3) PP wave space-time is known to give solvable background of string theory, and hence is very interesting background. We studied this geometry focusing on the supersymmetry aspects of the solution. Also systematic method is developed to derive various forms of p-brane ((p+1)-dimensional) action, and we plan to use the result to study quantization of p-branes.