Field Theory of Superstring and Heterotic String

超弦和异质弦的场论

基本信息

批准号：
02640225
负责人：
KUGO Taichi
金额：
$ 1.15万
依托单位：
Kyoto 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：
1990
资助国家：
日本
起止时间：
1990 至 1991
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-02640225/
关键词：
String field theory Target space duality Gauge transformation 3 Dimensional gravity Renormalizability Bethe-Salpeter equation pi meson Ward-Takahashi identity コンパクト化 SchwingerーDyson方程式非多項式閉弦場の理論ユニタリ-化処法 BRS不変性 1 N展開カイラル対称性

项目摘要

1. As a particular property of string, there is " target space duality" : for instance, the physics of the string on a torus space compe(ctified with radius R is the same as that on a torus with radius 1/R. This duality transformation R -> 1/R is known to be extended to the group 0(d, d ; Z)for the d-dimensional torus. I have shown in collaboration with B. Zwiebach that this 0(d, d ; Z)duality is essentially contained in the string field theory as a symmetry corresponding to particular gauge transformations.2. The fact is well-known that the pure gravity in 3 dimension is renormalizable. I have shown that the 3 dimensional gravity remains renormalizable even when matter fields are coupled to it, using 1IN expansion where N is the number of the matter fields. However, it turned out that a tachyon pole in the graviton propagator appears there. This implies that the used vacuum is unstable. I am still studying the implications and the method how to avoid this problem.3. In collaboration w … More ith Aoki, Bando and Mitchard, I have devised a method to cilcixlate the pion decay constant fpi using Higashijima, s improved ladder approximaiton to Bethe-Salpeter(BS)equation. We found that the Pagels-Stoker's approximate formula gives a rather good value for fpi. Using the similar approximaiton to BS equation, we also calculated the masses and decay constants of the lowest lying mesons in QCD such as rho, Ai and scalar mesons. The numerical results are found to reproduce the observed values surprisingly well. It was, however, discovered very receraly that the Higashijima approximation violates the chiral Ward-Takahashi(WT)identity. I have shown together with Michard that the chiral WT identity is preserved if the gluon momentum is used as the argument of the running coupling constant, and that it is necessary to use a non-local gauge with gauge parameter being a function of momentum in order for the scheme to be consistent with the ladder approximation. We have also confirmed that this consistent ladder approximation with non-local gauge reproduces almost the same numerical results for the physical quantities previously calculated. Less

1. 作为弦的一个特殊性质，存在“目标空间对偶性”：例如，弦在半径为 R 的环面空间上的物理性质与在半径为 1/R 的环面上的物理性质相同。已知变换 R -> 1/R 可以扩展到 d 维环面的群 0(d, d ; Z)，我与 B. Zwiebach 合作证明了这个 0(d, d ; Z)。 Z) 对偶性本质上包含在弦场论中，作为与特定规范变换相对应的对称性。2. 众所周知，3 维中的纯引力是可重整化的，即使当 3 维引力是可重整化的时。物质场与它耦合，使用 1IN 展开式，其中 N 是物质场的数量。然而，事实证明，引力子传播器中出现了一个快子极，这意味着所使用的真空是不稳定的。仍在研究其含义以及如何避免这个问题的方法。3.与 Aoki、Bando 和 Mitchard 合作，我设计了一种使用 Higashijima 改进的 Bethe-Salpeter 梯形近似来计算 π 介子衰变常数 fpi 的方法。 (BS) 方程。我们发现 Pagels-Stoker 的近似公式为 fpi 提供了相当好的值。 BS 方程中，我们还计算了 QCD 中最低介子（例如 rho、Ai 和标量介子）的质量和衰变常数，结果发现数值结果令人惊讶地很好地再现了观测值。东岛近似违反了手性 Ward-Takahashi(WT) 恒等式我与 Michard 一起证明，如果使用胶子动量作为参数，则手性 WT 恒等式得以保留。运行耦合常数，并且有必要使用规范参数为动量函数的非局部规范，以便使该方案与梯子近似一致。我们还证实了这种与非一致的梯子近似。本地仪表再现了与之前计算的物理量几乎相同的数值结果。