{
  "id": "math/0311058",
  "version": "v1",
  "published": "2003-11-05T09:34:17.000Z",
  "updated": "2003-11-05T09:34:17.000Z",
  "title": "Lectures on Instanton Counting",
  "authors": [
    "Hiraku Nakajima",
    "Kota Yoshioka"
  ],
  "comment": "60 pages, to appear in Proceedings of \"Workshop on algebraic structures and moduli spaces\", July 14 - 20, 2003, Centre de recherches mathematiques, Universite de Montreal",
  "categories": [
    "math.AG",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "These notes have two parts. The first is a study of Nekrasov's deformed partition functions $Z(\\ve_1,\\ve_2,\\vec{a};\\q,\\vec{\\tau})$ of N=2 SUSY Yang-Mills theories, which are generating functions of the integration in the equivariant cohomology over the moduli spaces of instantons on $\\mathbb R^4$. The second is review of geometry of the Seiberg-Witten curves and the geometric engineering of the gauge theory, which are physical backgrounds of Nekrasov's partition functions. The first part is continuation of math.AG/0306198, where we identified the Seiberg-Witten prepotential with $Z(0,0,\\vec{a};\\q,0)$. We put higher Casimir operators to the partition function and clarify their relation to the Seiberg-Witten $u$-plane. We also determine the coefficients of $\\ve_1\\ve_2$ and $(\\ve_1^2+\\ve_2^2)/3$ (the genus 1 part) of the partition function, which coincide with two measure factors $A$, $B$ appeared in the $u$-plane integral. The proof is based on the blowup equation which we derived in the previous paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-11-05T09:34:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "instanton counting",
      "susy yang-mills theories",
      "nekrasovs deformed partition functions",
      "higher casimir operators",
      "nekrasovs partition functions"
    ],
    "tags": [
      "lecture notes",
      "famous paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 60,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 632670,
      "adsabs": "2003math.....11058N"
    }
  }
}