{
  "id": "1311.2430",
  "version": "v3",
  "published": "2013-11-11T12:52:12.000Z",
  "updated": "2014-03-04T00:47:26.000Z",
  "title": "The $\\mathcal{N}=1$ Chiral Multiplet on $T^2\\times S^2$ and Supersymmetric Localization",
  "authors": [
    "Cyril Closset",
    "Itamar Shamir"
  ],
  "comment": "39 pages. v2: reference added; v3: corrected typos, JHEP version",
  "categories": [
    "hep-th"
  ],
  "abstract": "We compute the supersymmetric partition function of an $\\mathcal{N}=1$ chiral multiplet coupled to an external Abelian gauge field on complex manifolds with $T^2 \\times S^2$ topology. The result is locally holomorphic in the complex structure moduli of $T^2\\times S^2$. This computation illustrates in a simple example some recently obtained constraints on the parameter dependence of supersymmetric partition functions. We also devise a simple method to compute the chiral multiplet partition function on any four-manifold $\\mathcal{M}_4$ preserving two supercharges of opposite chiralities, via supersymmetric localization. In the case of $\\mathcal{M}_4=S^3\\times S^1$, we provide a path integral derivation of the previously known result, the elliptic gamma function, which emphasizes its dependence on the $S^3 \\times S^1$ complex structure moduli.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-03-04T00:47:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "supersymmetric localization",
      "supersymmetric partition function",
      "complex structure moduli",
      "chiral multiplet partition function",
      "external abelian gauge field"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/JHEP03(2014)040",
      "journal": "Journal of High Energy Physics",
      "year": 2014,
      "month": "Mar",
      "volume": 2014,
      "pages": 40
    },
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1264060,
      "adsabs": "2014JHEP...03..040C"
    }
  }
}