From double-scaled SYK correlators to Weil-Petersson volumes

Norman Do; Paul Norbury

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arXiv · 2511.21421

From double-scaled SYK correlators to Weil-Petersson volumes

Norman Do·Paul Norbury

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Abstract

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.

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Norman Do, Paul Norbury. 2025-11-26. From double-scaled SYK correlators to Weil-Petersson volumes. https://arxiv.org/abs/2511.21421

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