Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 20 (2024), 043, 86 pages      arXiv:2303.14154      https://doi.org/10.3842/SIGMA.2024.043

Some Generalizations of Mirzakhani's Recursion and Masur-Veech Volumes via Topological Recursions

Hiroyuki Fuji a and Masahide Manabe bc
a) Center for Mathematical and Data Sciences and Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan
b) Osaka Central Advanced Mathematical Institute, Osaka Metropolitan University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan
c) Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan

Received April 04, 2023, in final form May 09, 2024; Published online May 27, 2024

Abstract
Via Andersen-Borot-Orantin's geometric recursion, a twist of the topological recursion was proposed, and a recursion for the Masur-Veech polynomials was uncovered. The purpose of this article is to explore generalizations of Mirzakhani's recursion based on physical two-dimensional gravity models related to the Jackiw-Teitelboim gravity and to provide an introduction to various realizations of topological recursion. For generalized Mirzakhani's recursions involving a Masur-Veech type twist, we derive Virasoro constraints and cut-and-join equations, and also show some computations of generalized volumes for the physical two-dimensional gravity models.

Key words: topological recursion; Weil-Petersson volume; Masur-Veech volume; quantum Airy structure; Jackiw-Teitelboim gravity.

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