{
  "abstract": "We develop a cluster-algebraic description of symbol alphabets for chiral stress-tensor form factors in planar $\\mathcal N=4$ super-Yang--Mills theory. Motivated by unfolding the three-point $C_2$ quiver, we propose a periodic framework for $n$-point form-factor alphabets based on folding a $\\mathrm{Gr}(4,2n)$ quiver with two periods of frozen nodes. At four points, the folding leads to the $\\widetilde{\\mathrm{VI}}$ cluster algebra, which has infinitely many cluster variables. Tropical truncation selects a finite set of rational coordinates and four physical limit rays. The $A_1^{(1)}$ mutation sequences approaching these rays generate the four square roots and the corresponding algebraic-letter spaces. Within the resulting finite set of rational candidates, antipodal closure excludes precisely eight additional letters. On the parity-preserving surface, the antipodal map is realized, after a further folding, by two commuting mutations followed by a relabelling. Furthermore, we find an alternative quiver within the same mutation class that becomes self-antipodal after parity folding, mirroring the antipodal self-duality of the four-point MHV form factor. Its double- and triple-collinear boundaries reproduce, respectively, the $C_2$ algebra of the three-point form factor and the $A_3$ algebra of the six-point amplitude; after folding the latter to $C_2$, the antipodal map exchanges the two $C_2$ boundaries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04839",
  "author_total": 2,
  "authors": [
    {
      "name": "Song He"
    },
    {
      "name": "Jiahao Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e9m5fqwtpsddb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04839",
  "fulltext_url": null,
  "id": "e9m5fqwtpsddb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04839",
  "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|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7211890303",
  "pdf_url": "https://arxiv.org/pdf/2609.04839",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e9m5fqwtpsddb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:14Z",
      "native_id": "2609.04839",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04839"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Form Factor Alphabets and Antipodal Duality from Cluster Algebras",
  "title_text": "Form Factor Alphabets and Antipodal Duality from Cluster Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:14Z",
  "url": "https://research.draconitic.com/paper/e9m5fqwtpsddb",
  "venue": "arXiv",
  "versions": []
}