{
  "abstract": "We develop a new framework for evaluating higher-loop integrals for scalar fields on $S^D$. Starting from a Schwinger-parametric form for general higher-loop integrals on the sphere, it combines total-derivative identities with edge-contraction relations into a coupled linear system. To illustrate our method, we solve for all vacuum graphs through two loops. This includes, in particular, the two-loop three-melon, for which we construct the analytic solution for general $D$ and obtain explicit dimensionally regularized results at all integer dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30489",
  "author_total": 2,
  "authors": [
    {
      "name": "Varun Lochab"
    },
    {
      "name": "Frederik Denef"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a9pv82baf7snq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30489",
  "fulltext_url": null,
  "id": "a9pv82baf7snq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30489",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Particle physics theoretical and experimental studies"
    ]
  ],
  "openalex": "W7223265899",
  "pdf_url": "https://arxiv.org/pdf/2610.30489",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a9pv82baf7snq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2610.30489",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30489"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Higher-Loop Vacuum Integrals on $S^D$",
  "title_text": "Higher-Loop Vacuum Integrals on S^D",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:34Z",
  "url": "https://research.draconitic.com/paper/a9pv82baf7snq",
  "venue": "arXiv",
  "versions": []
}