Super volumes and KdV tau functions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912166556205056 |
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| author | Alexandrov, Alexander Norbury, Paul |
| author_facet | Alexandrov, Alexander Norbury, Paul |
| contents | 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 Brézin-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17272 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Super volumes and KdV tau functions Alexandrov, Alexander Norbury, Paul Algebraic Geometry High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems 14H10, 14D23, 32G15 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 Brézin-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. |
| title | Super volumes and KdV tau functions |
| topic | Algebraic Geometry High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems 14H10, 14D23, 32G15 |
| url | https://arxiv.org/abs/2412.17272 |