Field Theory of Superstring and Heterotic String

1.弦的一个特殊性质是“目标空间对偶”：例如，弦在半径为R的环面上的物理性质与半径为1/R的环面上的弦的物理性质相同。这种对偶变换R-1/R被推广到d维环面上的群0(d，d；Z)。我与B·兹维巴赫的合作表明，这种0(d，d；Z)对偶本质上包含在弦场理论中，作为对应于特定规范变换的对称性。众所周知，三维空间中的纯重力是可以重整化的。我已经证明，即使当物质场耦合到三维重力时，它仍然是可重整化的，使用1英寸展开，其中N是物质场的数量。然而，事实证明，在引力子传播子中出现了一个快子极。这意味着使用的真空是不稳定的。我还在研究这一问题的影响和如何避免这个问题。在与…协作中在Aoki，Bando和Mitchard的基础上，我设计了一种用Higashijima，S改进的阶梯近似计算Bethe-Salpeter(BS)方程的介子衰变常数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方程的近似方法，我们还计算了QCD中最底层介子如Rho、Ai和标量介子的质量和衰变常数。数值结果令人惊讶地重现了观测值。然而，最近发现东岛近似违背了手征Ward-Takahashi(WT)恒等式。我和Michard一起证明，如果胶子动量被用作运行耦合常数的自变量，手征WT恒等式是保持的，并且为了使方案与梯形近似一致，有必要使用规范参数是动量函数的非定域规范。我们还证实，这种与非定域规范一致的阶梯近似，对于先前计算的物理量来说，重现了几乎相同的数值结果。较少

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