{
  "id": "math/0505553",
  "version": "v1",
  "published": "2005-05-25T23:03:19.000Z",
  "updated": "2005-05-25T23:03:19.000Z",
  "title": "Instanton counting on blowup. II. $K$-theoretic partition function",
  "authors": [
    "Hiraku Nakajima",
    "Kota Yoshioka"
  ],
  "comment": "26 pages, no figures",
  "categories": [
    "math.AG",
    "hep-th"
  ],
  "abstract": "We study Nekrasov's deformed partition function of 5-dimensional supersymmetric Yang-Mills theory compactified on a circle. Mathematically it is the generating function of the characters of the coordinate rings of the moduli spaces of instantons on $\\mathbb R^4$. We show that it satisfies a system of functional equations, called blowup equations, whose solution is unique. As applications, we prove (a) logarithm of the partition function times $\\epsilon_1\\epsilon_2$ is regular at $\\epsilon_1 = \\epsilon_2 = 0$, (a part of Nekrasov's conjecture), and (b) the genus 1 parts, which are first several Taylor coefficients of the logarithm of the partition function, are written explicitly in terms of the Seiberg-Witten curves in rank 2 case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-05-25T23:03:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D21",
      "57R57",
      "81T13",
      "81T60"
    ],
    "keywords": [
      "theoretic partition function",
      "instanton counting",
      "study nekrasovs deformed partition function",
      "partition function times",
      "taylor coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 683464,
      "adsabs": "2005math......5553N"
    }
  }
}