{
  "id": "1206.4150",
  "version": "v2",
  "published": "2012-06-19T08:49:06.000Z",
  "updated": "2012-10-01T06:42:33.000Z",
  "title": "Conformal algebra: R-matrix and star-triangle relation",
  "authors": [
    "D. Chicherin",
    "S. Derkachov",
    "A. P. Isaev"
  ],
  "comment": "Added references and corrected typos",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP"
  ],
  "abstract": "The main purpose of this paper is the construction of the R-operator which acts in the tensor product of two infinite-dimensional representations of the conformal algebra and solves Yang-Baxter equation. We build the R-operator as a product of more elementary operators S_1, S_2 and S_3. Operators S_1 and S_3 are identified with intertwining operators of two irreducible representations of the conformal algebra and the operator S_2 is obtained from the intertwining operators S_1 and S_3 by a certain duality transformation. There are star-triangle relations for the basic building blocks S_1, S_2 and S_3 which produce all other relations for the general R-operators. In the case of the conformal algebra of n-dimensional Euclidean space we construct the R-operator for the scalar (spin part is equal to zero) representations and prove that the star-triangle relation is a well known star-triangle relation for propagators of scalar fields. In the special case of the conformal algebra of the 4-dimensional Euclidean space, the R-operator is obtained for more general class of infinite-dimensional (differential) representations with nontrivial spin parts. As a result, for the case of the 4-dimensional Euclidean space, we generalize the scalar star-triangle relation to the most general star-triangle relation for the propagators of particles with arbitrary spins.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-01T06:42:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conformal algebra",
      "r-operator",
      "representations",
      "nontrivial spin parts",
      "general star-triangle relation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/JHEP04(2013)020",
      "journal": "Journal of High Energy Physics",
      "year": 2013,
      "month": "Apr",
      "volume": 2013,
      "pages": 20
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1118757,
      "adsabs": "2013JHEP...04..020C"
    }
  }
}