{
  "id": "0903.2595",
  "version": "v1",
  "published": "2009-03-16T14:22:34.000Z",
  "updated": "2009-03-16T14:22:34.000Z",
  "title": "Introduction to Integral Discriminants",
  "authors": [
    "A. Morozov",
    "Sh. Shakirov"
  ],
  "comment": "36 pages, 19 figures",
  "journal": "JHEP 0912:002,2009",
  "doi": "10.1088/1126-6708/2009/12/002",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP"
  ],
  "abstract": "The simplest partition function, associated with homogeneous symmetric forms S of degree r in n variables, is integral discriminant J_{n|r}(S) = \\int e^{-S(x_1 ... x_n)} dx_1 ... dx_n. Actually, S-dependence remains the same if e^{-S} in the integrand is substituted by arbitrary function f(S), i.e. integral discriminant is a characteristic of the form S itself, and not of the averaging procedure. The aim of the present paper is to calculate J_{n|r} in a number of non-Gaussian cases. Using Ward identities -- linear differential equations, satisfied by integral discriminants -- we calculate J_{2|3}, J_{2|4}, J_{2|5} and J_{3|3}. In all these examples, integral discriminant appears to be a generalized hypergeometric function. It depends on several SL(n) invariants of S, with essential singularities controlled by the ordinary algebraic discriminant of S.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-16T14:22:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "introduction",
      "ordinary algebraic discriminant",
      "simplest partition function",
      "integral discriminant appears",
      "linear differential equations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "IOP",
      "journal": "Journal of High Energy Physics",
      "year": 2009,
      "month": "Dec",
      "volume": 2009,
      "number": 12,
      "pages": "002"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 815524,
      "adsabs": "2009JHEP...12..002M"
    }
  }
}