{
  "id": "math-ph/0304022",
  "version": "v1",
  "published": "2003-04-14T15:16:39.000Z",
  "updated": "2003-04-14T15:16:39.000Z",
  "title": "Classification of Two-dimensional Local Conformal Nets with c<1 and 2-cohomology Vanishing for Tensor Categories",
  "authors": [
    "Yasuyuki Kawahigashi",
    "Roberto Longo"
  ],
  "comment": "40 pages, LaTeX 2e",
  "journal": "Commun.Math.Phys.244:63-97,2004",
  "doi": "10.1007/s00220-003-0979-1",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "math.OA",
    "math.QA"
  ],
  "abstract": "We classify two-dimensional local conformal nets with parity symmetry and central charge less than 1, up to isomorphism. The maximal ones are in a bijective correspondence with the pairs of A-D-E Dynkin diagrams with the difference of their Coxeter numbers equal to 1. In our previous classification of one-dimensional local conformal nets, Dynkin diagrams D_{2n+1} and E_7 do not appear, but now they do appear in this classification of two-dimensional local conformal nets. Such nets are also characterized as two-dimensional local conformal nets with mu-index equal to 1 and central charge less than 1. Our main tool, in addition to our previous classification results for one-dimensional nets, is 2-cohomology vanishing for certain tensor categories related to the Virasoro tensor categories with central charge less than 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-04-14T15:16:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81T05",
      "81T40",
      "46L60",
      "18D10"
    ],
    "keywords": [
      "classification",
      "central charge",
      "one-dimensional local conformal nets",
      "classify two-dimensional local conformal nets",
      "virasoro tensor categories"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Communications in Mathematical Physics",
      "year": 2004,
      "month": "Jan",
      "volume": 244,
      "number": 1,
      "pages": 63
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 616945,
      "adsabs": "2004CMaPh.244...63K"
    }
  }
}