{
  "id": "1808.03295",
  "version": "v1",
  "published": "2018-08-09T18:26:53.000Z",
  "updated": "2018-08-09T18:26:53.000Z",
  "title": "Revisiting the computation of cohomology classes of the Witt algebra using conformal field theory and aspects of conformal algebra",
  "authors": [
    "Jacksyn Bakeberg",
    "Parthasarathi Nag"
  ],
  "comment": "Preliminary version with 26 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this article, we revisit some aspects of the computation of the cohomology class of $H^2 ( \\text{Witt}, \\mathbb{C})$ using some methods in two-dimensional conformal field theory and conformal algebra to obtain the one-dimensional central extension of the Witt algebra to the Virasoro algebra. Even though this is well-known in the context of standard mathematical physics literature, the operator product expansion of the energy-momentum tensor in two-dimensional conformal field theory is presented almost axiomatically. In this paper, we attempt to reformulate it with the help of a suitable modification of conformal algebra (as developed by V. Kac), and apply it to compute the representative element of the cohomology class which gives the desired central extension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-09T18:26:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81-02",
      "81T40",
      "81R10",
      "17B56",
      "17B68",
      "17B69"
    ],
    "keywords": [
      "conformal algebra",
      "cohomology class",
      "witt algebra",
      "two-dimensional conformal field theory",
      "computation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}