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    "paper_id": "3e440f74-ebe3-4097-a243-7b6bf74f1c87",
    "contributor_id": 3,
    "contributor_name": "ChenqiMeng",
    "base_hash": "20dee6044472681728e014a95dc0945d708c1caffc256551501e486ef7f21ac1",
    "title": "Vertex Operator Superalgebras and the Majorana Fermion",
    "authors": "Chenqi Meng",
    "abstract": "An introduction to vertex superalgebras and vertex operator superalgebras, with the free Majorana fermion as a worked example. The note develops signed identities, normal ordering, the Clifford realization, and the relation to the Ising VOA. Wick’s theorem gives Pfaffian formulas for vacuum correlation functions and for amplitudes with specified local coordinates. Regularized contractions encode descendant transformations and lead to efficient finite-matrix calculations. Further properties and computations are presented as exercises.",
    "markdown_sha256": "706c6b6195bff28dd7d1a2fbf0ed82c4ad6e8ddf092c6fc491074e2fa0e740ec",
    "explanation": "Separate local-coordinate amplitudes into Chapter 3. Start from the decorated-sphere vacuum amplitude defined by fields Y(W(f_i)a_i,z_i), following the local-coordinate convention in Meng–Lan–Gu, Appendix D.1. Prove fermion coordinate covariance and derive the generating identity Y(W(f_i)e^{uT}psi,z_i), with explicit inverse maps and fixed insertion points. Derive the regularized contractions and Pfaffian calculation from this definition. Keep the Majorana construction and basic Wick theorem in Chapter 2, update cross-references, and retain the exercises and CC BY 4.0 license.",
    "submitted_at": "2026-10-30T14:57:34.488281+00:00",
    "primary_category": "math.QA",
    "secondary_categories": [
      "math-ph"
    ],
    "license": "CC-BY-4.0",
    "agreement": {
      "version": "2026-10-19",
      "sha256": "12b437586e9f6a916c0b0d51430548ea47e644ef7d714f091056eb028088b106",
      "accepted_at": "2026-10-19T07:28:05.223110+00:00",
      "acceptance_id": 1
    },
    "chapters": [
      {
        "id": "definitions-and-properties",
        "title": "Definitions and properties",
        "markdown_sha256": "07485cb705564c1486410b5c6cb78daa875e6488d3922d413cdab8e94691b06f"
      },
      {
        "id": "majorana-fermion",
        "title": "The Majorana fermion",
        "markdown_sha256": "da9700e67f60cd37212bf657db1e444a76af50c84edb1e6e3da017de51b5775d"
      },
      {
        "id": "amplitudes-local-coordinates",
        "title": "Amplitudes with local coordinates",
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  "licensing": {
    "code": "CC-BY-4.0",
    "label": "CC BY 4.0",
    "url": "https://creativecommons.org/licenses/by/4.0/",
    "description": "Share and adapt, including commercially, with attribution and notice of changes.",
    "declaration": null
  }
}