arXiv 2002.083872020-02hep-thmath-phmath.MP

自举到字符串：求解正性随机矩阵模型

Bootstraps to Strings: Solving Random Matrix Models with Positivity

Henry W. Lin

备注：: 30 pages, 10 figures, 1 cartoon. See source for Mathematica notebook. v2: bootstrapped more complicated model, new Appendices. v3: journal version, v4: minor typos fixed
DOI：: 10.1007/JHEP06(2020)090

摘要：

本文提出了一种直接在大$N$极限下求解随机矩阵模型的新方法。首先，对一些低PT关联函数的一组数值进行了猜测。然后使用大的$N$环路方程来基于该猜测生成较高pt的关联函数的值。然后测试这些高PT功能是否与阳性要求一致，例如，$\langle \text{tr }M^{2k} \rangle \ge 0$。如果不是，则系统地排除猜测值。用这种方法，可以将随机矩阵的关联函数约束到一个包含（并且可能收敛于）真解的微小子区域。这种方法在单和多矩阵模型上进行了测试，并方便地再现了已知的解决方案。它也产生了强有力的结果，多矩阵模型，这是不被认为是可解的。一个诱人的可能性是，这种方法可以用来寻找新的临界点，或弦世界面理论。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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