1. Liouville Theory and the Weil-Petersson Geometry of Moduli Space
- Author
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Harrison, Sarah M., Maloney, Alexander, and Numasawa, Tokiro
- Subjects
High Energy Physics - Theory ,High Energy Physics - Theory (hep-th) ,FOS: Physical sciences - 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 $\mathcal M_{0,4}$ 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., Comment: 29+6 pages
- Published
- 2022
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