q-deformed Weil-Petersson Volumes from the Spectral Edge of DSSYK and Supersymmetric Extensions

@misc{ahmed2026qdeformed,
  title = {{$q$-deformed Weil-Petersson Volumes from the Spectral Edge of DSSYK and Supersymmetric Extensions}},
  author = {Wasif Ahmed and Joydeep Naskar and Krishan Saraswat},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13899},
  eprint = {2610.13899},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13899},
}

TY  - UNPB
TI  - q-deformed Weil-Petersson Volumes from the Spectral Edge of DSSYK and Supersymmetric Extensions
AU  - Wasif Ahmed
AU  - Joydeep Naskar
AU  - Krishan Saraswat
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13899
UR  - https://arxiv.org/abs/2610.13899
AB  - The q-deformed Weil-Petersson volumes of Do and Norbury are the top-degree parts of Okuyama's discrete volumes, which are defined by topological recursion on the spectral curve of the double-scaled SYK (DSSYK) model. We show that the same q-deformed volumes can be obtained from a double-scaled matrix model whose disk density is found by zooming in on the soft edges of the DSSYK density. Applying the same procedure to the hard edge of 𝒩=1 DSSYK, we obtain candidate q-deformed 𝒩=1 super Weil-Petersson volumes. They are polynomials of fixed degree, and they reduce to the 𝒩=1 super Weil-Petersson volumes in a scaled q→1 limit. These candidate volumes differ from the 𝒩=1 volumes of Do and Norbury in (arXiv:2510.12431) up to what we call "irrelevant" contributions which exactly vanish in the scaled q→ 1 limit. Together, these results demonstrate how q-deformed volumes can be naturally associated to the spectral edges of various DSSYK models and provides an intuitive way to construct them in supersymmetric contexts.
ER  -