{
  "id": "2111.12845",
  "version": "v2",
  "published": "2021-11-24T23:36:36.000Z",
  "updated": "2022-03-16T02:55:17.000Z",
  "title": "FZZ-triality and large $\\mathcal{N}=4$ super Liouville theory",
  "authors": [
    "Thomas Creutzig",
    "Yasuaki Hikida"
  ],
  "comment": "41 pages, minor modifications, references added, published version",
  "categories": [
    "hep-th"
  ],
  "abstract": "We examine dualities of two dimensional conformal field theories by applying the methods developed in previous works. We first derive the duality between $SL(2|1)_k/(SL(2)_k \\otimes U(1))$ coset and Witten's cigar model or sine-Liouville theory. The latter two models are Fateev-Zamolodchikov-Zamolodchikov (FZZ-)dual to each other, hence the relation of the three models is named FZZ-triality. These results are used to study correlator correspondences between large $\\mathcal{N}=4$ super Liouville theory and a coset of the form $Y(k_1,k_2)/SL(2)_{k_1 +k_2}$, where $Y(k_1 , k_2)$ consists of two $SL(2|1)_{k_i}$ and free bosons or equivalently two $U(1)$ cosets of $D(2,1;k_i -1)$ at level one. These correspondences are a main result of this paper. The FZZ-triality acts as a seed of the correspondence, which in particular implies a hidden $SL(2)_{k'}$ in $SL(2|1)_k$ or $D(2,1 ; k-1)_1$. The relation of levels is $k' -1 = 1/(k-1)$. We also construct boundary actions in sine-Liouville theory as another use of the FZZ-triality. Furthermore, we generalize the FZZ-triality to the case with $SL(n|1)_k/(SL(n)_k \\otimes U(1))$ for arbitrary $n>2$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-03-16T02:55:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "super liouville theory",
      "fzz-triality",
      "dimensional conformal field theories",
      "sine-liouville theory",
      "wittens cigar model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}