1. Liouville theory and the Weil-Petersson geometry of moduli space.
- Author
-
Harrison, Sarah M., Maloney, Alexander, and Numasawa, Tokiro
- Subjects
RIEMANN surfaces ,GEOMETRY ,RANDOM matrices ,SURFACE dynamics ,STATISTICS ,EIGENVALUES - Abstract
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 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. [ABSTRACT FROM AUTHOR]- Published
- 2023
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