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Unification Theory by Superstring Model and Early Cosmology

超弦模型和早期宇宙学的统一理论

基本信息

批准号：
61540209
负责人：
KIKKAWA Keiji
金额：
$ 0.96万
依托单位：
Faculty of Science, Osaka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1986
资助国家：
日本
起止时间：
1986 至 1987
项目状态：
已结题

项目摘要

The project started in 1986 to study two fundamental questions of the string and/or the superstring: (a) whether the string theory can be qualified as a theory of unifying the space-time geometry and fundamental interactions of the matter, and (b) whether the string theory provides us with any reasonable universe.We first questioned ourselves why the string is used as amodel of unification theory and none others such as the membrane, etc.. For any model to be the candidate, it must generate zero-mass particles (gauge bosons and graveion) in its spectum. We calculated the Casimir energy of membrane and showed that it never generates massless particles if the space-time dimensions are integers. This is supposed to be true except for the string.For the string to be qualified as the unification theory, the field theory of string must be formulated in a way that is geometry independent. We studied the cubic action model of string which was suggested by Friedan, Yoneya and Witten, and then m … More athematically formulated by Hata, Itoh, Kygo, Kunitomo and Ogawa, and Horowitz, Lykken, Rhom and Strominger. By solving the equation of motion derived from the cubic action, we proved that all the conformal invariant background metric fields (including torsion and dilaton), which derived in the non-linear sigma model approach, are the classical solutions of the cubic action as well. This shows that the cubic action model is indeed a non-trivial and selfcontained geometry independent field theory of string.In order to extend above ideas to the superstring we studied a number of properties of superstring amplitudes. Polyakov's path integral method, which has been extensively used in the above arguments, was applied to superstrings and showed that the supermoduli and the conformal Killing spinor play fundamental roles in the gauge anomaly cancellation. These practices in superstring are indispendable in our next project where the geometry independent field theory of superstring is to be studied. Less

该项目始于1986年，旨在研究弦和/或超弦的两个基本问题：(a)弦理论是否可以作为统一时空几何和物质基本相互作用的理论，以及(b)弦理论是否为我们提供了任何合理的宇宙。我们首先问自己，为什么用弦作为统一理论的模型，而不是用膜等其他模型。对于任何候选模型，它必须在其光谱中产生零质量粒子（规范玻色子和引力子）。我们计算了膜的卡西米尔能量，证明了在时空维度为整数的情况下，膜永远不会产生无质量粒子。这应该是真的，除了字符串。为了使弦具有统一理论的资格，弦的场论必须以一种与几何无关的方式表述。我们研究了由Friedan， Yoneya和Witten提出的弦的三次作用模型，然后由Hata， Itoh, Kygo， Kunitomo和Ogawa以及Horowitz， Lykken， Rhom和Strominger提出。通过求解由三次作用导出的运动方程，证明了在非线性sigma模型方法中导出的所有共形不变背景度量场（包括扭转和膨胀）也是三次作用的经典解。这表明三次作用模型确实是一个非平凡的、自包含的弦的几何独立场论。为了将上述思想推广到超弦，我们研究了超弦振幅的一些性质。将在上述论证中广泛使用的Polyakov路径积分方法应用于超弦，证明了超模和保角消旋量在规范异常对消中起着重要作用。这些在超弦上的实践在我们下一步研究超弦几何无关场论的项目中是不可缺少的。少