{
  "id": "1910.02033",
  "version": "v1",
  "published": "2019-10-04T16:50:55.000Z",
  "updated": "2019-10-04T16:50:55.000Z",
  "title": "Invariant subalgebras of the small $\\mathcal{N}=4$ superconformal algebra",
  "authors": [
    "Thomas Creutzig",
    "Andrew R. Linshaw",
    "Wolfgang Riedler"
  ],
  "comment": "32 pages",
  "categories": [
    "math.RT",
    "hep-th",
    "math.QA"
  ],
  "abstract": "Various aspects of orbifolds and cosets of the small $\\mathcal{N}=4$ superconformal algebra are studied. First, we determine minimal strong generators for generic and specific levels. As a corollary, we obtain the vertex algebra of global sections of the chiral de Rham complex on any complex Enriques surface. We also identify orbifolds of cosets of the small $\\mathcal{N}=4$ superconformal algebra with $\\text{Com}(V^{\\ell}(\\mathfrak{sl}_2), V^{\\ell+1}(\\mathfrak{sl}_2) \\otimes \\mathcal{W}_{-5/2}(\\mathfrak{sl}_4, f_{\\text{rect}}))$ and in addition at special levels with Grassmanian cosets and principal $\\mathcal{W}$-algebras of type $A$ at degenerate admissible levels. These coincidences lead us to a novel level-rank duality involving Grassmannian supercosets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-04T16:50:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "superconformal algebra",
      "invariant subalgebras",
      "determine minimal strong generators",
      "complex enriques surface",
      "novel level-rank duality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}