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Large genus asymptotics of super Weil-Petersson volumes

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arxiv 2501.07848 v1 pith:ZIF6VF5X submitted 2025-01-14 math.AG math-phmath.COmath.DGmath.MP

Xuanyu Huang This is my paper · ORCID
classification math.AGmath-phmath.COmath.DGmath.MP
keywords superasymptoticcoefficientsgenuslargeprovevolumesweil-petersson
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In this paper, we obtain the asymptotic expansions of super intersection numbers and prove that the associated coefficients are polynomials. Moreover, we give an algorithm which can explicitly compute these coefficients. As an application, we prove the existence of a complete asymptotic expansion of super Weil-Petersson volumes in the large genus. This generalizes the celebrated work of Mirzakhani-Zograf. We also confirm two conjectural formulae proposed by Griguolo-Papalini-Russo-Seminara.

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  1. Combinatorics and large genus asymptotics of the Br\'ezin--Gross--Witten numbers

    math-ph 2024-12 accept novelty 6.0 of 10

    The normalized Brézin-Gross-Witten numbers satisfy C(d) = 1/π + O(1/g(d)) uniformly in the number of marked points, with a polynomial structure in the large genus expansion.

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