String field theory and D-brane

我们研究了弦场理论和矩阵量子力学描述的亚临界量子引力。我们特别关注了开放弦扇区，其中d膜起着基本的作用。矩阵量子力学是用矩阵作为动力学自由度的量子力学系统来定义的。到目前为止，人们对闭弦扇区进行了研究。众所周知，这些自由度被简化为自由费米子，对它们进行广泛的研究是可能的。另一方面，与d膜相关的开放弦用所谓的非单重态扇区来描述。然后，系统由具有交互作用的Calogero系统管理。由于这种相互作用，对系统的分析变得更加困难，目前还没有很多研究。为了解决这一问题，本研究将注意力集中在守恒电荷的无限集上，并成功地构造了所有电荷对角化的态。通过这种方式，我们澄清了一直不太清楚的开放串扇区的可解性。我们还研究了3形式通量背景下的M（膜）理论。这是弦运动在两种形式通量存在下的推广。到目前为止，这个问题的研究被称为南部支架。在本研究中，我们研究了点状粒子的运动，它在通量中运动时会扩散。根据这个观察，我们可以定义描述粒子相互作用的顶点。我们还研究了在非交换空间中广泛研究的UV/IR混合。

We studied string field theory and the subcritical quantum gravity which is described by the matrix quantum mechanics. In particular, we focused on the open string sector where the D-brane plays the fundamental role. Matrix quantum mechanics is defined by the quantum mechanical system where matrix is used as the dynamical degree of freedom. So far, people have studied their closed string sector. These degree of freedom is known to be reduced to the free fermion and extensive study was possible for them. On the other hand, the open string which is related the D-brane is described by so called non-singlet sector. The system is then governed by the Calogero system with interactions. Because of this interaction, the analysis of the system becomes far more difficult and there have not been many studies. In order to treat this issue, in this study, we focused on the infinite set of conserved charges and succeeded to construct the states which diagonalize all the charges. In this way, we clarified the solvability of the open string sector which has not been so clear. We also studied M(embrane) theory in the 3 form flux background. This is a generalization of the string motion in the presence of two form flux. So far, this problem has been studied so called Nambu bracket. In this study, we have studied the motion of point like particle, which will spread when it moves in the flux. From this observation, we could define the vertex which describe the interaction of the particle. We also studied UV/IR mixing which was studied extensively in the noncommutative space to our background.