Higher Weil-Petersson volumes of the moduli space of super Riemann surfaces

TL;DR

This paper generalizes a recursion formula for Weil-Petersson volumes of super Riemann surfaces, inspired by JT supergravity, extending Mirzakhani's work to include higher degree kappa classes.

Contribution

It introduces a generalized recursion formula for Weil-Petersson volumes that incorporates high degree kappa classes in the context of super Riemann surfaces.

Findings

Derived a new recursion formula including kappa classes

Extended Mirzakhani's recursion to super Riemann surfaces

Provides tools for computing volumes in super moduli spaces

Abstract

Inspired by the theory of JT supergravity, Stanford-Witten derived a remarkable recursion formula of Weil-Petersson volumes of moduli space of super Riemann surfaces. It is the super version of the celebrated Mirzakhani's recursion formula. In this paper, we generalize Stanford-Witten's formula to include high degree kappa classes.