{
  "id": "1606.01041",
  "version": "v1",
  "published": "2016-06-03T10:54:41.000Z",
  "updated": "2016-06-03T10:54:41.000Z",
  "title": "Surface defects as transfer matrices",
  "authors": [
    "Kazunobu Maruyoshi",
    "Junya Yagi"
  ],
  "comment": "58 pages",
  "categories": [
    "hep-th",
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "The supersymmetric index of the 4d $\\mathcal{N} = 1$ theory realized by a brane tiling coincides with the partition function of an integrable 2d lattice model. We propose that a class of half-BPS surface defects in brane tiling models are represented on the lattice model side by transfer matrices constructed from L-operators. For the simplest surface defect in theories with $\\mathrm{SU}(2)$ flavor groups, we identify the relevant L-operator as that discovered by Sklyanin in the context of the eight-vertex model. We verify our proposal by computing the indices of class-$\\mathcal{S}$ and -$\\mathcal{S}_k$ theories in the presence of the surface defect.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-03T10:54:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "transfer matrices",
      "half-bps surface defects",
      "integrable 2d lattice model",
      "lattice model side",
      "simplest surface defect"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 58,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}