{
  "abstract": "We numerically construct the Sasaki--Einstein metric on the link of the cone over the second del Pezzo surface $\\mathrm{dP}_2$ and two primitive harmonic basic $(1,1)$-forms at its irregular volume-minimizing Reeb vector. Being toric, the metric in symplectic coordinates is encoded in a single convex function on a polygon. We approximate the correction to the canonical Guillemin potential in two ways: polynomial expansion and neural networks. The polynomial fit achieves a held-out mean-squared Monge--Ampère residual below $10^{-13}$, in contrast to the $10^{-2}$ plateau for the non-volume-minimizing regular Reeb vector. We validate our method against closed-form metrics of $Y^{p,q}$ using curvature invariants, and also against the numerical result of Doran et al. (2007) for the Kähler--Einstein metric of $\\mathrm{dP}_3$ using the Laplacian spectrum of low torus-invariant modes. The integrated Riemann-squared curvature of the $\\mathrm{dP}_2$ link agrees to two parts in $10^{9}$ with the closed form conjectured from the dual field theory. Our data for the metric and harmonic forms can be used to study warped non-conformal holographic IIB backgrounds, the analogues of the Klebanov--Tseytlin solution on the conifold.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25857",
  "author_total": 3,
  "authors": [
    {
      "name": "Nakwoo Kim"
    },
    {
      "name": "Sejin Kim"
    },
    {
      "name": "Hoseob Shin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4h8nxbqtmj130.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25857",
  "fulltext_url": null,
  "id": "4h8nxbqtmj130",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25857",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7214067292",
  "pdf_url": "https://arxiv.org/pdf/2609.25857",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4h8nxbqtmj130.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2609.25857",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25857"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Numerical Sasaki--Einstein metrics and harmonic forms on del Pezzo links",
  "title_text": "Numerical Sasaki--Einstein metrics and harmonic forms on del Pezzo links",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:31Z",
  "url": "https://research.draconitic.com/paper/4h8nxbqtmj130",
  "venue": "arXiv",
  "versions": []
}