The super Weil-Petersson asymptotic expansion and the coefficients
Abstract
We determine the universal constant in the large-genus asymptotic expansion of super Weil-Petersson volumes. The argument adopts the uniform-transport strategy for shifted theta intersection numbers. The uniform large-genus theorem for normalized BGW numbers of Guo-Norbury-Yang-Zagier determines the amplitude at a simpler endpoint. The result is C=π−9/2. We give a proof of the Griguolo-Papalini-Russo-Seminara conjecture for fixed boundary lengths and fixed descendant degrees. The boundary formula is uniform when the sum of the lengths is o(√g), and we exhibit an obstruction at the √g scale. We also compute the first four inverse-genus coefficients by two exact recursive methods and derive general polynomial structure results. Finally, we show that, for each fixed genus, the super Weil-Petersson volume divided by n! is a polynomial in the number n of marked points.
Related
- Eynard-Orantin Topological Recursions for Higher Weil-Petersson Volumes on Moduli Spaces of Super Riemann Surfaces
- A discrete analogue of 𝒩=2 super Weil-Petersson volumes
- Ramond from Random: Weil-Petersson Volumes for Super-Riemann surfaces with NS Boundaries and R Punctures
- Generalized Hitchin-Kobayashi correspondence and Weil-Petersson current
- Closed Response Calculus for SLE Weldings and Weil--Petersson Kähler Geometry
BibTeX
@misc{huang2026super,
title = {{The super Weil-Petersson asymptotic expansion and the coefficients}},
author = {Xuanyu Huang and Kefeng Liu and Hao Xu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06621},
eprint = {2611.06621},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06621},
}
RIS
TY - UNPB
TI - The super Weil-Petersson asymptotic expansion and the coefficients
AU - Xuanyu Huang
AU - Kefeng Liu
AU - Hao Xu
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06621
UR - https://arxiv.org/abs/2611.06621
AB - We determine the universal constant in the large-genus asymptotic expansion of super Weil-Petersson volumes. The argument adopts the uniform-transport strategy for shifted theta intersection numbers. The uniform large-genus theorem for normalized BGW numbers of Guo-Norbury-Yang-Zagier determines the amplitude at a simpler endpoint. The result is C=π^−9/2. We give a proof of the Griguolo-Papalini-Russo-Seminara conjecture for fixed boundary lengths and fixed descendant degrees. The boundary formula is uniform when the sum of the lengths is o(√g), and we exhibit an obstruction at the √g scale. We also compute the first four inverse-genus coefficients by two exact recursive methods and derive general polynomial structure results. Finally, we show that, for each fixed genus, the super Weil-Petersson volume divided by n! is a polynomial in the number n of marked points.
ER -