Studies on Numerical Quantization of the Gravity and the String Model

在本项目期间，我们取得了以下成果：(L)通过对环长分布的测量，发现了一种新的标度定律，并与票价协议的理论进行了比较。(2)通过测量世界表面的正规性，发现该表面在中心电荷大于1的情况下是不稳定的。(3)对二维表面统计性质的研究表明，表面可分为光滑、粗糙和支化聚合物三种类型。(4)在与二维表面相似的数学模型中，测量了三维和四维表面的可观测值，发现普适标度与维度无关。(5)在弦磁化率中发现了大的有限尺寸效应后，我们用巨正则方法重新进行了计算，得到了与理论一致的结果。在此基础上，我们继续对(L)超弦和(2)与U(L)规范场耦合的四维引力的研究。

During the period of this project we have achieved the following results : (l)From the measurement of loop-length distribution a novel scaling law was found and later compared to theory with fare agreement. (2)By measuring the registivity of the world surface the surface was found to be unstable above the central charge larger than 1 as predicted by the analytic theory.(3)Studies of the statistical property of two dimensional surface reveal that surfaces are classified into three types, namely smooth, rough and branched polymer. (4)Measuring observables for 3 and 4 dimensional surface in the similar maimer as 2 dimensional surface we found the universal scaling independent of the dimensionarity. (5)After the finding of large finite size effects in string susceptibility, we calculate it again by the grandeanonical method and obtain fare agreement with theory Based on these results we are continuing our investigation on (l)the super-string and (2)the 4D gravity coupled to the U(l) gauge field.