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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

该项目于 1986 年开始，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弦被用作统一理论的模型，而不是膜等其他模型。对于任何模型作为候选模型，它必须在其光谱中产生零质量粒子（规范玻色子和重力粒子）。我们计算了膜的卡西米尔能量，并表明如果时空维度是整数，它永远不会产生无质量粒子。除了弦之外，这应该是正确的。为了将弦限定为统一理论，必须以与几何无关的方式来表述弦的场论。我们研究了 Friedan、Yoneya 和 Witten 提出的弦的立方作用模型，然后由 Hata、Itoh、Kygo、Kunitomo 和 Okawa、Horowitz、Lykken、Rhom 和 Strominger 数学公式化。通过求解由三次作用导出的运动方程，我们证明了用非线性西格玛模型方法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。这表明立方作用模型确实是一个非平凡的、独立于几何的弦场论。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。波利亚科夫的路径积分方法在上述论证中得到了广泛的应用，该方法被应用于超弦，并表明超模和共形 Killing 旋量在规范异常抵消中发挥着重要作用。在我们的下一个项目中，超弦的这些实践是不可或缺的，我们将研究超弦的几何独立场论。较少的