{
  "abstract": "Magic relations are a class of integration-by-parts identities where all integrals in the generating sector drop out. Since their presence causes several otherwise successful methods in the Feynman-integral computational pipeline to break down, they are important to detect and understand. In this paper, we take a first step toward a systematic characterization of such identities. Specifically, we observe and argue that the occurrence of magic relations always coincides with the presence of higher-dimensional critical varieties in the generating sector. This provides a practical computational test to check if a family of Feynman integrals can contain magic relations and to find them, which we implement in the ancillary Mathematica file Magic-Test.m. Additionally, we discuss how to count the number of master integrals in the presence of higher-dimensional critical varieties, classify the behavior of magic relations under symmetries, and we discuss their interplay with cuts.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.29789",
  "author_total": 4,
  "authors": [
    {
      "name": "Giulio Crisanti"
    },
    {
      "name": "Hjalte Frellesvig"
    },
    {
      "name": "Andrzej Pokraka"
    },
    {
      "name": "Sid Smith"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bk7t5252nw83g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.29789",
  "fulltext_url": null,
  "id": "bk7t5252nw83g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.29789",
  "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-ph"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3106|Particle physics theoretical and experimental studies"
    ]
  ],
  "openalex": "W7162755033",
  "pdf_url": "https://arxiv.org/pdf/2605.29789",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bk7t5252nw83g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2605.29789",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.29789"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Magic Relations and Critical Varieties of Feynman Integrals",
  "title_text": "Magic Relations and Critical Varieties of Feynman Integrals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/bk7t5252nw83g",
  "venue": "arXiv",
  "versions": []
}