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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弦场论对D-胚的解释，第一年（2001年）我从边界共形场论的角度考察开弦星星积与D-胚的投影算符之间的关系开始研究。在其他投影仪中，我们研究了身份，银和蝴蝶运营商，并认为身份运营商似乎是最有前途的，因为它正确地再现了弦张力。然而，与此同时，他意识到在开弦中点的奇点阻止了严格的治疗。在第二年（2002年）。我开始发展开弦场论的正则化版本，它基于简化的星星积，Moyal积，它在非对易几何中被广泛使用。在这种语言中，我发现奇点表现为星星乘积的结合性的异常。我们无法逃离异常点 ...更多信息只要我们处理无穷多个分量，并且我们通过将分量域截断为有限个来引入正则化方案。利用这个公式，我们可以对所有的离壳层振幅进行可靠的计算，同时，我们也可以对快子真空进行解析研究。离壳振幅的计算是相当令人满意的，因为我们可以写在有限秩矩阵的显式形式的所有振幅。同时，我们认识到，从中点的奇异性实际上是占主导地位的快子真空的计算。在这个意义上，我们认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。我们知道D-膜最好用闭弦扇区中的边界态来描述。我们证明了所有已知的边界态都满足一个普适的幂等关系，它与VSFT运动方程的形式完全相同。少