{
  "id": "1810.00928",
  "version": "v1",
  "published": "2018-10-01T19:29:55.000Z",
  "updated": "2018-10-01T19:29:55.000Z",
  "title": "Stacky dualities for the moduli of Higgs bundles",
  "authors": [
    "Richard Derryberry"
  ],
  "comment": "32 pages",
  "categories": [
    "math.AG",
    "hep-th",
    "math.RT"
  ],
  "abstract": "The central result of this paper is an identification of the shifted Cartier dual of the moduli stack $\\mathcal{M}_{\\mathfrak{g}}(C)$ of $\\widetilde{G}$-Higgs bundles on $C$ of arbitrary degree (modulo shifts by $Z(\\widetilde{G})$) with a quotient of the Langlands dual stack $\\mathcal{M}_{^L\\mathfrak{g}}(C)$. Via hyperk\\\"ahler rotation, this may equivalently be viewed as the identification of an SYZ fibration relating Hitchin systems for arbitrary Langlands dual semisimple groups, coupled to nontrivial finite $B$-fields. As a corollary certain self-dual stacks $\\frac{\\mathcal{M}_{\\mathfrak{g}}(C)}{\\Gamma}$ are observed to exist, which I conjecture to be the Coulomb branches for the 3d reduction of the 4d $\\mathcal{N}=2$ theories of class $\\mathcal{S}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-01T19:29:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D24"
    ],
    "keywords": [
      "higgs bundles",
      "stacky dualities",
      "arbitrary langlands dual semisimple groups",
      "syz fibration relating hitchin systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}