2024/05/17 by Adrien Sauvaget, Sauvaget, Adrien
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Advanced Algebra and Geometry #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2405.10869
Volumes of moduli spaces of hyperbolic cone surfaces were previously defined and computed when the angles of the cone singularities are at most 2pi. We propose a general definition of these volumes without restriction on the angles. This construction is based on flat geometry as our proposed volume is a limit of Masur-Veech volumes of moduli spaces of multi-differentials. This idea generalizes the observation in quantum gravity that the Jackiw-Teitelboim partition function is a limit of minimal string partition functions from Liouville gravity. Finally, we use the properties of these volumes to recover Mirzakhani's recursion formula for Weil-Petersson polynomials. This provides a new proof of Witten-Kontsevich's theorem.