Quantum study of ground state and black holes in superstring theories

本研究项目取得了以下成果：(1)研究弦理论中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坐标与空间坐标之间的非交换性，而且研究了空间坐标与时间坐标之间的非交换性，为这些理论的非摄动分析奠定了基础。进一步，我们明确地考察了三维理论在对偶条件下的变换性质。我们还研究了这些理论中作为孤子解实现的d膜周围的超对称性和涨落谱。作为本工作的推广，我们证明了在非平凡背景下，D膜系统和反D膜系统存在不破缺的超对称。本文还阐明了孤子的模空间，并用结果来检验孤子的散射。(2)时间相关解对于研究黑洞形成和弦论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/或开弦理论是在膜上实现的。我们也给出了大多数一般的随时间变化的膜解。它们是内部空间大小随时间变化的精确解，它们给出了非常有趣的膨胀宇宙学模型。他们给出了非常有希望的模型来解释目前正在加速膨胀的宇宙，并吸引了很多人的注意。(3) PP波时空给出了弦理论的可解背景，是一个非常有趣的背景。我们研究了这种几何，重点是解决方案的超对称方面。我们还开发了系统的方法来推导各种形式的p膜（（p+1）维）作用，并计划利用这一结果来研究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.