Unification Theory by Superstring Model and Early Cosmology

该项目始于1986年，研究弦和/或超弦的两个基本问题：(A)弦理论是否可以被限定为一种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。我们首先质疑自己，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Casimir能量，结果表明，当时空维度为整数时，膜不会产生无质量粒子。为了使弦成为统一理论，弦的场论必须以一种几何无关的方式来表述。我们研究了Friedan，Yoneya和Witten提出的弦的立方作用力模型，并在此基础上提出了m…由Hata、Itoh、Kygo、Kuritomo和Ogawa，以及Horowitz、Lykken、RHOM和Strominger更具主题的配方。通过求解由立方作用量导出的运动方程，证明了在非线性Sigma模型方法中得到的所有共形不变背景度量场(包括挠率和伸缩子)也是立方作用量的经典解。这表明立方作用量模型确实是一种非平凡的、自包含的弦的几何无关场理论。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Polyakov的路径积分方法应用于超弦，证明了超模和共形Killing旋量在规范反常抵消中起着重要作用。在我们的下一个项目中，超弦的这些实践是不可缺少的，我们将研究超弦的几何无关场理论。较少

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