A q-analogue of Mirzakhani's recursion for Weil-Petersson volumes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917012075184128 |
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| author | Do, Norman Norbury, Paul |
| author_facet | Do, Norman Norbury, Paul |
| contents | We define q-analogues of Mirzakhani's recursion for Weil-Petersson volumes and the Stanford-Witten recursion for super Weil-Petersson volumes. Okuyama recently introduced a q-deformation of the Gaussian Hermitian matrix model which produces quasi-polynomials that recover the Weil-Petersson volumes via a rescaled q to 1 limit. The q-deformations of the Weil-Petersson volumes produced here agree with the top degree terms of Okuyama's quasi-polynomials and suggest a variation of Okuyama's methods to the super setting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_12431 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A q-analogue of Mirzakhani's recursion for Weil-Petersson volumes Do, Norman Norbury, Paul Algebraic Geometry High Energy Physics - Theory Mathematical Physics 14H10, 14D23, 32G15 We define q-analogues of Mirzakhani's recursion for Weil-Petersson volumes and the Stanford-Witten recursion for super Weil-Petersson volumes. Okuyama recently introduced a q-deformation of the Gaussian Hermitian matrix model which produces quasi-polynomials that recover the Weil-Petersson volumes via a rescaled q to 1 limit. The q-deformations of the Weil-Petersson volumes produced here agree with the top degree terms of Okuyama's quasi-polynomials and suggest a variation of Okuyama's methods to the super setting. |
| title | A q-analogue of Mirzakhani's recursion for Weil-Petersson volumes |
| topic | Algebraic Geometry High Energy Physics - Theory Mathematical Physics 14H10, 14D23, 32G15 |
| url | https://arxiv.org/abs/2510.12431 |