{
  "id": "1406.4290",
  "version": "v2",
  "published": "2014-06-17T09:30:13.000Z",
  "updated": "2014-09-19T16:12:14.000Z",
  "title": "Conformal field theory on the plane",
  "authors": [
    "Sylvain Ribault"
  ],
  "comment": "118 pages. Public domain. Share your own version of this text at https://github.com/ribault/CFT-Review . Version 2: numerous small improvements",
  "categories": [
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We provide an introduction to conformal field theory on the plane in the conformal bootstrap approach. We introduce the main ideas of the bootstrap approach to quantum field theory, and how they apply to two-dimensional theories with local conformal symmetry. We describe the mathematical structures which appear in such theories, from the Virasoro algebra and its representations, to the BPZ equations and their solutions. As examples, we study a number of models: Liouville theory, (generalized) minimal models, free bosonic theories, the $H_3^+$ model, and the $SU_2$ and $\\widetilde{SL}_2(\\mathbb{R})$ WZW models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-17T09:30:13.000Z",
      "comment": "115 pages. Share your own version of this text at https://github.com/ribault/CFT-Review",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-19T16:12:14.000Z"
    }
  ],
  "analyses": {
    "themes": [
      {
        "category": "hep-th",
        "topics": [
          "conformal field theory"
        ]
      }
    ],
    "keywords": [
      "conformal field theory",
      "conformal bootstrap",
      "Virasoro algebra",
      "BPZ equations",
      "Liouville theory",
      "minimal models",
      "free bosons"
    ],
    "tags": [
      "review article",
      "github project"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 118,
      "language": "en",
      "license": "Public Domain",
      "status": "editable",
      "inspire": 1300839,
      "adsabs": "2014arXiv1406.4290R"
    }
  }
}