{
  "id": "2103.12611",
  "version": "v1",
  "published": "2021-03-23T15:09:40.000Z",
  "updated": "2021-03-23T15:09:40.000Z",
  "title": "Surface defects in gauge theory and KZ equation",
  "authors": [
    "Nikita Nekrasov",
    "Alexander Tsymbaliuk"
  ],
  "comment": "38 pages, 2 figures",
  "categories": [
    "hep-th",
    "math.AG",
    "math.QA",
    "math.RT"
  ],
  "abstract": "We study the regular surface defect in the $\\Omega$-deformed four dimensional supersymmetric gauge theory with gauge group $SU(N)$ with $2N$ hypermultiplets in fundamental representation. We prove its vacuum expectation value obeys the Knizhnik-Zamolodchikov equation for the $4$-point conformal block of the $\\widehat{\\mathfrak{sl}}_{N}$-current algebra, originally introduced in the context of two dimensional conformal field theory. The level and the vertex operators are determined by the parameters of the $\\Omega$-background and the masses of the hypermultiplets, the cross-ratio of the $4$ points is determined by the complexified gauge coupling. We clarify that in a somewhat subtle way the branching rule is parametrized by the Coulomb moduli. This is an example of the BPS/CFT relation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-23T15:09:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32G34"
    ],
    "keywords": [
      "kz equation",
      "dimensional supersymmetric gauge theory",
      "dimensional conformal field theory",
      "vacuum expectation value obeys",
      "somewhat subtle way"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}