{
  "id": "1806.08344",
  "version": "v1",
  "published": "2018-06-21T17:44:10.000Z",
  "updated": "2018-06-21T17:44:10.000Z",
  "title": "Irregular conformal blocks and connection formulae for Painlevé V functions",
  "authors": [
    "O. Lisovyy",
    "H. Nagoya",
    "J. Roussillon"
  ],
  "comment": "26 pages, 1 figure",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove a Fredholm determinant and short-distance series representation of the Painlev\\'e V tau function $\\tau(t)$ associated to generic monodromy data. Using a relation of $\\tau(t)$ to two different types of irregular $c=1$ Virasoro conformal blocks and the confluence from Painlev\\'e VI equation, connection formulas between the parameters of asymptotic expansions at $0$ and $i\\infty$ are conjectured. Explicit evaluations of the connection constants relating the tau function asymptotics as $t\\to 0,+\\infty,i\\infty$ are obtained. We also show that irregular conformal blocks of rank 1, for arbitrary central charge, are obtained as confluent limits of the regular conformal blocks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-21T17:44:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "irregular conformal blocks",
      "connection formulae",
      "painleve vi equation",
      "virasoro conformal blocks",
      "short-distance series representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}