String Field Theory and D-brane Dynamics

本课题1998-2000年三个学年的研究成果如下：无取向开闭弦系统的弦场理论：给出了开闭弦混合系统的弦场理论的一个全阶作用，并给出了它的BRS不变性的完整证明。识别出异常单环图，期望能消除异常。在课程中，我们证明了由Peskin等人提出的GGRT（广义胶合平滑定理）的一个广义版本2。超对称E_6大统一模型：我们利用反常U(1)对称构造了一个包含Frogatt-Nielsen机制的超对称E_6大统一模型，该模型可以一致地解释夸克、轻子和中微子扇区的所有质量矩阵。在分析质量矩阵的过程中，我们发现了一个有趣的新关系，它在经验上很好地证明了大轻子混合角与夸克质量和混合角之间的关系。膜世界场景：我们指出了我们的世界所在的3膜涨落模态的重要性，并证明了当膜张力较小时，体规场的高Kaluza-Klein模态的耦合被指数抑制。通过评价脉动模式对第五力和超新星冷却过程的贡献，我们得到了膜张力的下界。作为认真研究膜世界情景的准备工作，我们首先从已知的6维超共形张量演算中导出了5维超重力张量演算，然后明确计算了5维超重力耦合的物质和Yang-Mills超多重态的一般系统的不变量作用。

The research results of our project for three academic years in 1998-2000 are as follows :1. String field theory of unoriented open-closed string system : We presented a full order action of the string field theory for the mixed system of open and closed strings and gave a complete proof for its BRS invariance. Anomalous one-loop graphs are identified which are expected to cancel the anomaly. In the course, we proved a generalized version of the GGRT (generalized gluing resmoothing theorem) by Peskin et al.2. Supersymmetric E_6 grand unified model : We constructed a supersymmetric E_6 grand unified model which incorporates the Frogatt-Nielsen mechanism using anomalous U (1) symmetry and can consistently explain all the mass matrices of quark, lepton and neutrino sectors. In the process of analyzing mass matrices, we found an interesting novel relation which holds remarkably well empirically and relates the large lepton mixing angle to the quark masses and a mixing angle.3. Brane world scenario : We pointed out the imporatance of the fluctuation mode of the 3-brane on which our world lies, and proved that the couplings of the higher Kaluza-Klein modes of the bulk gauge field are exponentially suppressed if the brane tension is small. Evaluating the contributions of the fluctuation mode to the fifth force and the supernova cooling process, we obtained the lower bound for the brane tension. As a preparation for investigating the brane world scenario seriously, we first derived a supergravity tensor calculus in 5 dimensions from the known 6-dimensional superconformal tensor calculus, and then explicitly calculated and invariant action for the general system of matter and Yang-Mills supermultiplets coupled to supergravity in 5 dimensions.