{
  "id": "1811.01577",
  "version": "v1",
  "published": "2018-11-05T09:52:39.000Z",
  "updated": "2018-11-05T09:52:39.000Z",
  "title": "Chiral algebras of class $\\mathcal{S}$ and Moore-Tachikawa symplectic varieties",
  "authors": [
    "Tomoyuki Arakawa"
  ],
  "categories": [
    "math.RT",
    "hep-th",
    "math.QA"
  ],
  "abstract": "We give a functorial construction of the genus zero chiral algebras of class $\\mathcal{S}$, that is, the vertex algebras corresponding to the theory of class $\\mathcal{S}$ associated with genus zero pointed Riemann surfaces via the 4d/2d duality discovered by Beem, Lemos, Liendo, Peelaers, Rastelli and van Rees. We show that there is a unique family of vertex algebras satisfying the required conditions and show that they are all simple and conformal. In fact, our construction works for any complex semisimple group G that is not necessarily simply laced. Furthermore, we show that the associated varieties of these vertex algebras are exactly the genus zero Moore-Tachikawa symplectic varieties that have been recently constructed by Braverman, Finkelberg and Nakajima using the geometry of the affine Grassmannian for the Langlands dual group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-05T09:52:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vertex algebras",
      "genus zero moore-tachikawa symplectic varieties",
      "genus zero pointed riemann surfaces",
      "genus zero chiral algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}