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弦在半径为1/R的环面上的物理性质相同。已知这种对偶变换R -> 1/R可以推广到d维环面的群0（d，d ; Z）。我已经与B合作展示了这一点。Zwiebach认为，这种0（d，d ; Z）对偶性本质上包含在弦场论中，作为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化的。我已经证明了，即使当物质场耦合到它时，三维引力仍然是可重整化的，使用1 IN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快子极出现在那里。这意味着所使用的真空是不稳定的。我仍在研究的含义和方法如何避免这个问题。3.合作W ...更多信息 本文与Aoki，Bando和Mitchard一起，设计了一种用东岛改进的阶梯近似计算π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值fpi。利用与BS方程类似的近似，我们还计算了QCD中最低位介子如ρ介子、Ai介子和标量介子的质量和衰变常数。数值结果发现，再现观测值令人惊讶的好。然而，最近发现，Higashijima近似违反了手征Ward-Takahashi（WT）恒等式。我已经与Michard一起证明了，如果胶子动量被用作运行耦合常数的自变量，手征WT恒等式是保持不变的，并且为了使该方案与阶梯近似一致，有必要使用规范参数是动量的函数的非定域规范。我们还证实，这种一致的阶梯近似与非局域规范重现几乎相同的数值结果的物理量以前计算。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