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PreprintCC BY 4.0arXiv

A discrete analogue of 𝒩=2 super Weil-Petersson volumes

  • Wasif Ahmed
  • Joydeep Naskar
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Abstract

We introduce a discrete spectral curve from 𝒩=2 double-scaled SYK whose topological recursion defines quasi-polynomial volumes in integer boundary lengths. The curve has two edge theories: a local 𝒩=2 theory at the lower edge and a bosonic theory at the upper edge. Focusing on the local 𝒩=2 theory, we compute its finite-q volumes and independently check the first few using the string equation. In the qβ†’ 1 continuum limit, these recover the super Weil-Petersson volumes of Turiaci and Witten. Finally, we give an all-genus intersection-theoretic interpretation of these local volumes on the moduli space of stable marked curves, in terms of a deformed spin class with a gap-dependent ΞΊ-class dressing.

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Cite

BibTeXRIS
BibTeX
@misc{ahmed2026discrete,
  title = {{A discrete analogue of $\mathscrN=2$ super Weil-Petersson volumes}},
  author = {Wasif Ahmed and Joydeep Naskar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13667},
  eprint = {2610.13667},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13667},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A discrete analogue of 𝒩=2 super Weil-Petersson volumes
AU  - Wasif Ahmed
AU  - Joydeep Naskar
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13667
UR  - https://arxiv.org/abs/2610.13667
AB  - We introduce a discrete spectral curve from 𝒩=2 double-scaled SYK whose topological recursion defines quasi-polynomial volumes in integer boundary lengths. The curve has two edge theories: a local 𝒩=2 theory at the lower edge and a bosonic theory at the upper edge. Focusing on the local 𝒩=2 theory, we compute its finite-q volumes and independently check the first few using the string equation. In the qβ†’ 1 continuum limit, these recover the super Weil-Petersson volumes of Turiaci and Witten. Finally, we give an all-genus intersection-theoretic interpretation of these local volumes on the moduli space of stable marked curves, in terms of a deformed spin class with a gap-dependent ΞΊ-class dressing.
ER  -