{
  "abstract": "In this paper, we review the Zamolodchikov-like recursion relations for torus one-point conformal blocks in both Liouville and $A_2$ Toda theories. Starting from these relations, we derive the corresponding recursion relations in the light asymptotic limit. In Liouville theory, the light-limit recursion reproduces the known expression for the one-point light conformal block in terms of the Gauss hypergeometric function. For $A_2$ Toda theory, our recursion relation provides a new, efficient method for explicit calculations, and we have verified that it is in full agreement with previously known results in the literature. Last but not least, we present closed-form expressions for the coefficients of the insertion-point expansion for both the generic and light $A_2$ Toda one-point blocks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.09177",
  "author_total": 2,
  "authors": [
    {
      "name": "Armen Poghosyan"
    },
    {
      "name": "Hasmik Poghosyan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d1t7reffr9sjr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.09177",
  "fulltext_url": null,
  "id": "d1t7reffr9sjr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.09177",
  "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",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7168179870",
  "pdf_url": "https://arxiv.org/pdf/2607.09177",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d1t7reffr9sjr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2607.09177",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.09177"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "A note on Zamolodchikov's recursion relation for the torus conformal block and its light limit",
  "title_text": "A note on Zamolodchikov's recursion relation for the torus conformal block and its light limit",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:48Z",
  "url": "https://research.draconitic.com/paper/d1t7reffr9sjr",
  "venue": "arXiv",
  "versions": []
}