Large genus asymptotics of super Weil-Petersson volumes

TL;DR

This paper derives asymptotic expansions for super Weil-Petersson volumes in large genus, introduces an algorithm for computing related coefficients, and confirms conjectural formulas, extending Mirzakhani-Zograf's work.

Contribution

It provides the first complete asymptotic expansion of super Weil-Petersson volumes and verifies two conjectures in the field.

Findings

Asymptotic expansions of super intersection numbers are obtained.

An explicit algorithm for computing polynomial coefficients is developed.

Confirmation of two conjectural formulas related to super Weil-Petersson volumes.

Abstract

In this paper, we obtain the asymptotic expansions of super intersection numbers and prove that the associated coefficients are polynomials. Moreover, we give an algorithm which can explicitly compute these coefficients. As an application, we prove the existence of a complete asymptotic expansion of super Weil-Petersson volumes in the large genus. This generalizes the celebrated work of Mirzakhani-Zograf. We also confirm two conjectural formulae proposed by Griguolo-Papalini-Russo-Seminara.