Geometry of String Theory and Its Nonperturbative Effect

弦论几何及其非微扰效应

基本信息

批准号：
13640267
负责人：
MATSUO Yutaka
金额：
$ 2.05万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2003
项目状态：
已结题

项目摘要

The focus of the research in these three years is the interpretation of D-brane in terms of the string field theory.In the first year (2001), I started the research by examining the relation between the projection operators of the open string star product and D-brane in the viewpoint of the boundary conformal field theory. Among other projectors, we examined identity, sliver and butterfly operators anc argued that the identity operator seems the most promising one since it reproduces the string tension correctly. At the same time, however, realized that a singularity at the midpoint of the open string prevents the rigorous treatment.In the second year (2002). I began to develop a regularized version of the open string field theory based on the simplified star product, Moyal product, which is used extensively in the noncommutative geometry. In this language, I found that the singularity appears as an anomaly of the Associativity of the star product. We can not escape from the anomaly as … More long as we work with the infinite number of components and we introduced a regularization scheme by cutting off the component field to the finite number. With this reformulation, we can make a reliable computation of all the off-shell amplitudes: At the same time, we can also make an analytic study of the tachyon vacuum. The computation of off-shell amplitude is quite satisfactory since we can write all the amplitudes in the explicit form with finite rank matrices. At the same time, we realized that the singularity from the midpoint is actually dominant to the computation of the tachyon vacuum. In this sense, we realized that open string language is not appropriate to describe the D-brane.Finally, we start to analyze the D-brane in the closed string language. It is known that D-brane is best described by the boundary state which live in the closed string sector. We show that all the known boundary state satisfy a universal idempotency relation, which has exactly the same form of the VSFT equation of motion. Less

这三年的研究重点是用弦场论解释D-膜。第一年（2001年），我从研究开弦星积的投影算子之间的关系开始研究从边界共形场理论的角度来看，我们研究了恒等算子、条子算子和蝶形算子，并认为恒等算子似乎是最有前途的，因为它可以正确地再现弦张力。然而，意识到开弦中点的奇点阻碍了严格的处理。第二年（2002年）我开始开发基于简化明星积Moyal积的正则化版本的开弦场理论，主要用于在这种语言中，我发现奇点表现为星积结合律的异常，只要我们处理无限数量的组件，我们就无法摆脱这种异常。通过将分量场截断为有限数的正则化方案，我们可以对所有离壳振幅进行可靠的计算：同时，我们还可以对快子真空进行分析研究。离壳振幅的计算结果非常令人满意，因为我们可以用有限秩矩阵将所有振幅写成显式形式。同时，我们意识到中点的奇异性实际上对快子的计算起着主导作用。从这个意义上说，我们意识到开弦语言不适合描述D-膜。最后，我们开始分析闭弦语言中的D-膜。众所周知，D-膜最好用闭弦语言来描述。我们证明所有已知的边界状态都满足通用幂等关系，其形式与 VSFT Less 运动方程完全相同。