论文标题
引导到字符串：求解具有积极性的随机矩阵模型
Bootstraps to Strings: Solving Random Matrix Models with Positivity
论文作者
论文摘要
开发了一种直接在大$ n $限制中求解随机矩阵模型的新方法。首先，猜测了某些低位相关函数的一组数值。然后，大型$ n $循环方程用于基于此猜测生成高点相关函数的值。然后，人们测试这些高点功能是否与阳性要求一致，例如$ \ langle \ text {tr} m^{2k} \ rangle \ ge 0 $。如果没有，猜测的值将被系统排除。这样，一个人可以将随机矩阵的相关函数限制为一个微小的子区域，该区域包含（甚至收敛到）真实解决方案。该方法在单个和多矩阵模型上进行了测试，并便利地复制已知的解决方案。它还为多矩阵模型产生了强劲的结果，这些模型被认为是无法解决的。诱人的可能性是，该方法可用于搜索新的关键点或字符串世界表理论。
A new approach to solving random matrix models directly in the large $N$ limit is developed. First, a set of numerical values for some low-pt correlation functions is guessed. The large $N$ loop equations are then used to generate values of higher-pt correlation functions based on this guess. Then one tests whether these higher-pt functions are consistent with positivity requirements, e.g., $\langle \text{tr }M^{2k} \rangle \ge 0$. If not, the guessed values are systematically ruled out. In this way, one can constrain the correlation functions of random matrices to a tiny subregion which contains (and perhaps converges to) the true solution. This approach is tested on single and multi-matrix models and handily reproduces known solutions. It also produces strong results for multi-matrix models which are not believed to be solvable. A tantalizing possibility is that this method could be used to search for new critical points, or string worldsheet theories.
