Super volumes and KdV tau functions

Alexander Alexandrov; Paul Norbury

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arXiv · 2412.17272

Super volumes and KdV tau functions

Alexander Alexandrov·Paul Norbury

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Abstract

Weil-Petersson volumes of the moduli space of curves are deeply related to the Kontsevich-Witten KdV tau function. They possess a Virasoro symmetry which comes out of recursion relations between the volumes due to Mirzakhani. Similarly, the super Weil-Petersson volumes of the moduli space of super curves with Neveu-Schwarz punctures are related to the Br\'ezin-Gross-Witten (BGW) tau function of the KdV hierarchy and satisfy a recursion due to Stanford and Witten, analogous to Mirzakhani's recursion. In this paper we prove that by also allowing Ramond punctures, the super Weil-Petersson volumes are related to the generalised BGW KdV tau function, which is a one parameter deformation of the BGW tau function. This allows us to prove that these new super volumes also satisfy the Stanford-Witten recursion.

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Alexander Alexandrov, Paul Norbury. 2024-12-23. Super volumes and KdV tau functions. https://arxiv.org/abs/2412.17272

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