We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Liouville theory and the Weil-Petersson geometry of moduli space.
- Authors
Harrison, Sarah M.; Maloney, Alexander; Numasawa, Tokiro
- 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.
- Subjects
RIEMANN surfaces; GEOMETRY; RANDOM matrices; SURFACE dynamics; STATISTICS; EIGENVALUES
- Publication
Journal of High Energy Physics, 2023, Vol 2023, Issue 11, p1
- ISSN
1126-6708
- Publication type
Article
- DOI
10.1007/JHEP11(2023)227