Field Theory of Superstring and Heterotic String

1. 弦的一个特殊性质是“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半径为1/R的环面上的物理性质相同。这个对偶变换R -> 1/R可以扩展到d维环面的群0（d, d； Z）。我已经与B. Zwiebach合作证明了这个0（d, d； Z）对偶本质上包含在弦场理论中，作为一种对应于特定规范变换的对称性。众所周知，三维纯引力是可重整的。我已经证明了三维重力仍然是可重整的，即使当物质场与它耦合时，使用1IN展开，其中N是物质场的数量。然而，事实证明，引力子传播子中的速子极出现在那里。这意味着所用的真空是不稳定的。我还在研究它的含义和如何避免这个问题的方法。在与Aoki， Bando和Mitchard的合作中，我设计了一种利用Higashijima改进的阶梯近似于beth - salpeter （BS）方程来计算介子衰变常数fpi的方法。我们发现Pagels-Stoker的近似公式给出了一个相当好的fpi值。利用类似于BS方程的近似，我们还计算了QCD中最底层介子的质量和衰变常数，如rho、Ai和标量介子。结果表明，数值模拟结果与观测值的拟合效果相当好。然而，人们很晚才发现，Higashijima近似违反手性Ward-Takahashi（WT）恒等式。我已经和Michard一起证明，如果胶子动量被用作运行耦合常数的参数，手性WT恒等是保留的，并且有必要使用一个非局部规范，规范参数是动量的函数，以便方案与阶梯近似一致。我们还证实，这种非局部规范的一致阶梯近似对先前计算的物理量再现了几乎相同的数值结果。少

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