{
  "id": "math/0205236",
  "version": "v1",
  "published": "2002-05-23T18:57:18.000Z",
  "updated": "2002-05-23T18:57:18.000Z",
  "title": "Mirror symmetry, Langlands duality, and the Hitchin system",
  "authors": [
    "Tamas Hausel",
    "Michael Thaddeus"
  ],
  "comment": "31 pages, LaTeX with packages amsfonts, latexsym, [dvips]graphicx, [dvips]color, one embedded postscript figure",
  "doi": "10.1007/s00222-003-0286-7",
  "categories": [
    "math.AG",
    "hep-th",
    "math-ph",
    "math.DG",
    "math.MP"
  ],
  "abstract": "We study the moduli spaces of flat SL(r)- and PGL(r)-connections, or equivalently, Higgs bundles, on an algebraic curve. These spaces are noncompact Calabi-Yau orbifolds; we show that they can be regarded as mirror partners in two different senses. First, they satisfy the requirements laid down by Strominger-Yau-Zaslow (SYZ), in a suitably general sense involving a B-field or flat unitary gerbe. To show this, we use their hyperkahler structures and Hitchin's integrable systems. Second, their Hodge numbers, again in a suitably general sense, are equal. These spaces provide significant evidence in support of SYZ. Moreover, they throw a bridge from mirror symmetry to the duality theory of Lie groups and, more broadly, to the geometric Langlands program.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-05-23T18:57:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H60",
      "14D21",
      "14H40",
      "14H70",
      "32S35"
    ],
    "keywords": [
      "mirror symmetry",
      "langlands duality",
      "hitchin system",
      "suitably general sense",
      "geometric langlands program"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 587392
    }
  }
}