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    "format": "peerpedia-submission-v4",
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    "paper_id": "34fac3d3-7f8c-40b5-b5c3-59163f46e8ad",
    "contributor_id": 3,
    "contributor_name": "ChenqiMeng",
    "base_hash": "ffe122dca3bcf80f4a4341bce5c933f404ffec409660f813f1a5da01821108ed",
    "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": "71008aa074acb2bea900155a7a72e95195bf069798c0a06d2015963a341ddb48",
    "explanation": "Add fields of Virasoro descendants to the VOA chapter. Prove the iterate formula with explicit Jacobi residues, define normal ordering using A_+ and A_-, and express negative-mode descendants as normal-ordered derivatives of the conformal field. Define multiple normal ordering by right nesting, explain that associativity is not assumed, and give the repeated-descendant formula with the explicit mode recursion in the proof. Preserve all other chapters.",
    "submitted_at": "2026-10-30T03:05:48.217084+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": "d551a16fd743f5a7f52975fe24ecb5692606de9ee4d23840970a6ee56209eaf4"
      },
      {
        "id": "vertex-operator-algebras",
        "title": "Vertex operator algebras",
        "markdown_sha256": "b3c14cc371c39ae145619542194920a95bd3812c6f4073f42d04a431f3b70a86"
      },
      {
        "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": "1041c5031ebc9fe9a068b27eac02a6e06aa5eca7c47949f79f5c12521e9129ab"
      },
      {
        "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
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}