Studies on the quantum gravity effects in the early universe and black holes via string field theory and D-branes

我们研究了非对易空间上的三维引力理论，其中只有一个宇宙学常数项作为包含量子引力效应的模型。我们得到了对应于时空气泡或插值零度规、Minkowski度规等的各种解。我们得到的所有解在非对易参数中都是非微扰的，因此被认为与量子引力密切相关。我们还研究了模糊圆盘，它是非对易平面上的圆盘状区域。我们证明，通过使用量子光学中已知的相位算符和相位态，可以将角度的概念引入模糊圆盘。作为应用，我们构造了模糊圆盘上标量场理论的扇形孤子解，它可能对应于扇形D膜。我们还将这一概念应用到激光物理的非对易实验中。

We investigated a three-dimensional gravitational theory on a noncommutative space which has a cosmological constant term only as a model which includes quantum gravity effects. We obtained various solutions that correspond to bubbles of spacetimes or interpolates zero metric and Minkowski metric and so on. All solutions we obtained are non-perturbative in the noncommutative parameter, therefore they are thought to be closely related to quantum gravity.We also investigated the fuzzy disc, which is a disc-shaped region in a noncommutative plane. We showed that one can introduce a concept of angles to the fuzzy disc, by using the phase operator and phase states known in quantum optics. As an application, we constructed fan-shaped soliton solutions of a scalar field theory on a fuzzy disc, which might correspond to a fan-shaped D-brane. We also applied this concept to an experimental test of noncommutativity by laser physics.