论文标题
通过低维量子重力的通用随机矩阵相关性来限制Weil-Petersson体积
Constraining Weil-Petersson volumes by universal random matrix correlations in low-dimensional quantum gravity
论文作者
论文摘要
基于2019年Saad，Saad，Shenker和Stanford的Jackiw-teitelboim量子重力与双刻度矩阵的发现之间的二元性，我们在2019年在通用随机矩阵理论（RMT）中的两种理论之间的一致性如何限制了对模块化模块空间的大量约束的限制。这些卷是根据多项式函数（Weil-petersson卷）给出的，它解决了众所周知的非线性递归公式，众所周知，该公式很难分析。由于我们的结果意味着Weil-Petersson卷的系数之间的线性关系，因此它们既为其符号计算，也提供了简化其构造的可能方法。通过这种方式，我们提出了一个长期计划，以通过使用通用RMT结果作为输入来提高对双曲线歧管模量空间的数学困难方面的理解。
Based on the discovery of the duality between Jackiw-Teitelboim quantum gravity and a double-scaled matrix ensemble by Saad, Shenker and Stanford in 2019, we show how consistency between the two theories in the universal Random Matrix Theory (RMT) limit imposes a set of constraints on the volumes of moduli spaces of Riemannian manifolds. These volumes are given in terms of polynomial functions, the Weil-Petersson volumes, solving a celebrated nonlinear recursion formula that is notoriously difficult to analyze. Since our results imply linear relations between the coefficients of the Weil-Petersson volumes, they therefore provide both a stringent test for their symbolic calculation and a possible way of simplifying their construction. In this way, we propose a long-term program to improve the understanding of mathematically hard aspects concerning moduli spaces of hyperbolic manifolds by using universal RMT results as input.
