论文标题
liouville理论和模量空间的Weil-Petersson几何形状
Liouville Theory and the Weil-Petersson Geometry of Moduli Space
论文作者
论文摘要
Liouville理论描述了具有恒定负曲率的表面的动力学，可用于研究Riemann表面模量空间的Weil-Petersson几何形状。这导致了一种有效的算法，以使用Zamolodchikov的递归关系来计算Weil--Petersson指标将其用于任意准确性。例如，我们通过在带有四个穿刺的球体上考虑liouville理论来计算$ \ MATHCAL M_ {0,4} $在数值上至高准确度上的度量。我们从数字上计算Weil-Petersson Laplacian的特征值，并发现证据表明高斯正交集合中随机基质的统计数据。
Liouville theory describes the dynamics of surfaces with constant negative curvature and can be used to study the Weil-Petersson geometry of the moduli space of Riemann surfaces. This leads to an efficient algorithm to compute the Weil--Petersson metric to arbitrary accuracy using Zamolodchikov's recursion relation for conformal blocks. For example, we compute the metric on $\mathcal M_{0,4}$ numerically to high accuracy by considering Liouville theory on a sphere with four punctures. We numerically compute the eigenvalues of the Weil-Petersson Laplacian, and find evidence that the obey the statistics of a random matrix in the Gaussian Orthogonal Ensemble.
