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    "submission_id": "07345724-d384-4560-ad45-41d03dce6e69",
    "paper_id": "34fac3d3-7f8c-40b5-b5c3-59163f46e8ad",
    "contributor_id": 3,
    "contributor_name": "ChenqiMeng",
    "base_hash": "4b5a5ae729fbcf69a6f87dcffdae8a4e0cb4f3c4d0d9b22394af59dba0b0e600",
    "title": "Introduction to Vertex Operator Algebras",
    "authors": "Chenqi Meng",
    "abstract": "Vertex operator algebra is a rigorous formulation of 2D chiral conformal field theory. This note reviews (will do!) its definition, construction, and properties. It in particular emphasizes the field (mathematics)-like properties of a VOA. A VOA can be viewed as a quantized field. We will eventually (hopefully) arrive at the quantum Galois theory of VOA.",
    "markdown_sha256": "09f5aa725f258ea53b36e6ad558d2f52fe2b6a7f2c3da29f4753e556803ed309",
    "explanation": "Add the rank-one Heisenberg VOA as the first worked example, following the notation of the local Heisenberg note. Construct the oscillator space and state-field correspondence, prove the conformal structure with an explicit calculation of central charge one, and establish simplicity. Record the first weight spaces and trivial zero-mode action, with exercises on reflection and composite products. Preserve the lattice and minimal-model outlines and all other chapters.",
    "submitted_at": "2026-10-30T03:49:56.496378+00:00",
    "primary_category": "math.QA",
    "secondary_categories": [],
    "license": "CC0-1.0",
    "agreement": {
      "version": "2026-10-19",
      "sha256": "12b437586e9f6a916c0b0d51430548ea47e644ef7d714f091056eb028088b106",
      "accepted_at": "2026-10-19T07:28:05.223110+00:00",
      "acceptance_id": 1
    },
    "chapters": [
      {
        "id": "about-this-note",
        "title": "About this note",
        "markdown_sha256": "e129af1e12b564976535a6cf671334e2e26059aee4ac1266bbf90fe779b57d4b"
      },
      {
        "id": "vertex-algebras",
        "title": "Vertex algebras",
        "markdown_sha256": "c8cbb13deb8cd9eb287d33179f182ceb07cccb819091178fc4f7c9c54f9de372"
      },
      {
        "id": "vertex-operator-algebras",
        "title": "Vertex operator algebras",
        "markdown_sha256": "b1999c78e5257dd32455b354d1db6008996b440fd7d4f3aabc0b9d42a2f14438"
      },
      {
        "id": "constructions",
        "title": "Basic structure of VOAs",
        "markdown_sha256": "692053fdeaa5cd76ac8e7f593b0a8352f85e1878c12888ede040a734775881a8"
      },
      {
        "id": "orbifolds",
        "title": "G-orbifolds",
        "markdown_sha256": "e155dd89c549102449aa82463e19aed200b56ffab8360b90c508414aa43b4313"
      },
      {
        "id": "cosets",
        "title": "Commutants and cosets",
        "markdown_sha256": "249f6c1af80e73888edf39614b16c3412a2d3b3201d1fd870120d405aad4412b"
      },
      {
        "id": "examples",
        "title": "Examples of VOAs",
        "markdown_sha256": "d81c5f09f5c85b54ac2fd6a5574e8615d126baeccd7b5886c3334b562f7c5809"
      },
      {
        "id": "correlation-functions",
        "title": "Chiral correlation functions",
        "markdown_sha256": "915a637dc27b1a98d4f2ff519418227c5b3077d5ae8dfde50f72436f4df01159"
      },
      {
        "id": "modules",
        "title": "Modules and intertwining operators",
        "markdown_sha256": "871265dff96061879b1043ffa4a96caf4160999fd3b86790b402123fb2df09fb"
      },
      {
        "id": "tensor-categories",
        "title": "Vertex tensor categories",
        "markdown_sha256": "ea3cc4c149d8793faeb3cb3d4f1a6962aca839a2a123fc4b2ae2d65ad06c7aee"
      },
      {
        "id": "extensions",
        "title": "Extensions and quantum Galois theory",
        "markdown_sha256": "38c2ebc58642fa3cc00c09863fa0adde86ecb045c75f39ffc967589e3ded3978"
      }
    ],
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  "licensing": {
    "code": "CC0-1.0",
    "label": "CC0 1.0",
    "url": "https://creativecommons.org/publicdomain/zero/1.0/",
    "description": "Dedicate the work to the public domain to the extent legally possible. Reuse does not require attribution under CC0.",
    "declaration": null
  }
}