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

2025/01/10 by Huang, Xuanyu, Liu, Kefeng, Xu, Hao
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2501.05806

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.

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• Super volumes and KdV tau functions
• A Simple Recursion for the Mirzakhani Volume and its Super Extension
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• Super Weil-Petersson measures on the moduli space of curves