From double-scaled SYK correlators to Weil-Petersson volumes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908677147983872 |
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| author | Do, Norman Norbury, Paul |
| author_facet | Do, Norman Norbury, Paul |
| contents | Okuyama introduced a family of polynomials, whose coefficients depend on a parameter $q$, in his study of correlators in the double-scaled SYK model. He verified in small cases that their coefficients can be expressed in terms of certain $q$-zeta values and that the polynomials recover the Weil-Petersson volumes of moduli spaces studied by Mirzakhani under a certain $q \to 1$ limit. In this paper, we provide mathematically rigorous proofs of these two phenomena. The authors previously defined natural $q$-deformations of the Weil-Petersson volumes of moduli spaces of curves. We prove that these polynomials appear as the top degree part of Okuyama's polynomials. Our work provides a link between the two topics of the title, which hints at a ``quantum'' Weil-Petersson geometry and a combinatorial-geometric approach to double-scaled SYK correlators. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_21421 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From double-scaled SYK correlators to Weil-Petersson volumes Do, Norman Norbury, Paul Algebraic Geometry Mathematical Physics 14H10, 32G15, 81T32 Okuyama introduced a family of polynomials, whose coefficients depend on a parameter $q$, in his study of correlators in the double-scaled SYK model. He verified in small cases that their coefficients can be expressed in terms of certain $q$-zeta values and that the polynomials recover the Weil-Petersson volumes of moduli spaces studied by Mirzakhani under a certain $q \to 1$ limit. In this paper, we provide mathematically rigorous proofs of these two phenomena. The authors previously defined natural $q$-deformations of the Weil-Petersson volumes of moduli spaces of curves. We prove that these polynomials appear as the top degree part of Okuyama's polynomials. Our work provides a link between the two topics of the title, which hints at a ``quantum'' Weil-Petersson geometry and a combinatorial-geometric approach to double-scaled SYK correlators. |
| title | From double-scaled SYK correlators to Weil-Petersson volumes |
| topic | Algebraic Geometry Mathematical Physics 14H10, 32G15, 81T32 |
| url | https://arxiv.org/abs/2511.21421 |