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    "paper_id": "34fac3d3-7f8c-40b5-b5c3-59163f46e8ad",
    "contributor_id": 3,
    "contributor_name": "ChenqiMeng",
    "base_hash": "03344a2883a9830b338d1cf5189cfbf134a92c146880f7c0ce32a5c93c6fead1",
    "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": "1792567925bef9eaf3c23664ddc99e8dd2892abef807646134be2430a2afc4d8",
    "explanation": "Add the super Jacobi identity to the VSA exercises with explicit parity and expansion conventions, and derive the field supercommutator by residue. Add Majorana vacuum correlations, prove the Wick/Pfaffian formula from Clifford modes, give the four-point formula and differentiated contractions, and include a stress-tensor two-point exercise. Changes are confined to the VOSA chapter.",
    "submitted_at": "2026-10-30T10:02:31.011173+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": "0ee3a3f27b8ed47fcfe89c570fbc70747f9c697fe38c577779040a658cd74fde"
      },
      {
        "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": "96506c552e532224b8ca6893f4e12422caf6a8ca143a930e58292a21a30fdae1"
      },
      {
        "id": "vertex-operator-superalgebras",
        "title": "Vertex operator superalgebras",
        "markdown_sha256": "af4b61a1c8df1020c12d9efe8ccb003a9beb3058f5bbd78e9fbda792add67e36"
      },
      {
        "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
  }
}