{
  "id": "1404.0659",
  "version": "v1",
  "published": "2014-04-02T19:15:02.000Z",
  "updated": "2014-04-02T19:15:02.000Z",
  "title": "Stability and integration over Bergman metrics",
  "authors": [
    "Semyon Klevtsov",
    "Steve Zelditch"
  ],
  "comment": "24 pages, 3 figures",
  "journal": "JHEP07(2014)100",
  "doi": "10.1007/JHEP07(2014)100",
  "categories": [
    "hep-th",
    "math-ph",
    "math.DG",
    "math.MP"
  ],
  "abstract": "We study partition functions of random Bergman metrics, with the actions defined by a class of geometric functionals known as `stability functions'. We introduce a new stability invariant - the critical value of the coupling constant - defined as the minimal coupling constant for which the partition function converges. It measures the minimal degree of stability of geodesic rays in the space the Bergman metrics, with respect to the action. We calculate this critical value when the action is the $\\nu$-balancing energy, and show that $\\gamma_k^{\\rm crit} = k - h$ on a Riemann surface of genus $h$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-02T19:15:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integration",
      "partition function converges",
      "critical value",
      "study partition functions",
      "random bergman metrics"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Journal of High Energy Physics",
      "year": 2014,
      "month": "Jul",
      "volume": 2014,
      "pages": 100
    },
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1288340,
      "adsabs": "2014JHEP...07..100K"
    }
  }
}