{
  "abstract": "We develop a probabilistic construction of Toda field theory correlators from the Coulomb gas representation. Reinterpreting $n$-point functions of primaries as $w$-moments of random variables with respect to a Gaussian measure, we derive constraints on the Toda momenta and coupling constant. $L^2$ and $L^p$ convergence conditions for the associated random variables, triviality constraints on the correlators, and local integrability conditions for the cross-moments are derived. These constraints define an extended region of convergence for the Toda correlators and provide a systematic, probabilistic interpretation of the Seiberg bounds. We proceed to analytically continue the moment indices by employing a Mellin-Barnes representation of the random variables. The local convergence boundaries become meromorphic local integrability divisors, and, in the semiclassical $b\\to0$ limit, these divisors reconstruct the Liouville charge pole lattice. For $A_n$ Toda theory, we show that natural $W_n$-closure conditions in this semiclassical limit select rank-one, Virasoro-like submodules inside the full Toda theory. On these slices, the scalar integrability conditions reduce to Liouville-like divisors and recover the corresponding Toda charge pole lattices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22717",
  "author_total": 2,
  "authors": [
    {
      "name": "Jacques Distler"
    },
    {
      "name": "Bahaa Elshimy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8r1ekxjc6cnxh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22717",
  "fulltext_url": null,
  "id": "8r1ekxjc6cnxh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22717",
  "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": "W7214018737",
  "pdf_url": "https://arxiv.org/pdf/2609.22717",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8r1ekxjc6cnxh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.22717",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22717"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Semiclassical reconstruction of the Toda pole lattice via analytic continuation of the Probabilistic Approach",
  "title_text": "Semiclassical reconstruction of the Toda pole lattice via analytic continuation of the Probabilistic Approach",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/8r1ekxjc6cnxh",
  "venue": "arXiv",
  "versions": []
}