{
  "id": "1512.01802",
  "version": "v1",
  "published": "2015-12-06T15:39:14.000Z",
  "updated": "2015-12-06T15:39:14.000Z",
  "title": "Conformal Ward and BPZ Identities for Liouville quantum field theory",
  "authors": [
    "Antti Kupiainen",
    "Rémi Rhodes",
    "Vincent Vargas"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this work, we continue the constructive probabilistic approach to the Liouville Quantum Field theory (LQFT) started in \\cite{DKRV}. We give a rigorous construction of the stress energy tensor in LQFT and prove the validity of the conformal Ward identities. Within this framework, we also derive the Belavin-Polyakov-Zamolodchikov (BPZ) differential equations of order 2 for the associated degenerate fields of the theory. As an application, we give an explicit formula for the 4 point correlation function with a degenerate field insertion leading to a proof of a non trivial functional relation on the 3 point structure constant derived earlier by Teschner.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-06T15:39:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "81T40",
      "81T20"
    ],
    "keywords": [
      "liouville quantum field theory",
      "bpz identities",
      "conformal ward",
      "non trivial functional relation",
      "point structure constant derived earlier"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1408592
    }
  }
}