{
  "id": "1601.01559",
  "version": "v1",
  "published": "2016-01-07T15:14:17.000Z",
  "updated": "2016-01-07T15:14:17.000Z",
  "title": "The continuum limit of $a_{N-1}^{(2)}$ spin chains",
  "authors": [
    "Eric Vernier",
    "Jesper Lykke Jacobsen",
    "Hubert Saleur"
  ],
  "comment": "43 pages, 4 figures",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "hep-th",
    "math.MP"
  ],
  "abstract": "Building on our previous work for $a_2^{(2)}$ and $a_3^{(2)}$ we explore systematically the continuum limit of gapless $a_{N-1}^{(2)}$ vertex models and spin chains. We find the existence of three possible regimes. Regimes I and II for $a_{2n-1}^{(2)}$ are related with $a_{2n-1}^{(2)}$ Toda, and described by $n$ compact bosons. Regime I for $a_{2n}^{(2)}$ is related with $a_{2n}^{(2)}$ Toda and involves $n$ compact bosons, while regime II is related instead with $B^{(1)}(0,n)$ super Toda, and involves in addition a single Majorana fermion. The most interesting is regime III, where {\\sl non-compact} degrees of freedom appear, generalising the emergence of the Euclidean black hole CFT in the $a_{2}^{(2)}$ case. For $a_{2n}^{(2)}$ we find a continuum limit made of $n$ compact and $n$ non-compact bosons, while for $a_{2n-1}^{(2)}$ we find $n$ compact and $n-1$ non-compact bosons. We also find deep relations between $a_{N-1}^{(2)}$ in regime III and the gauged WZW models $SO(N)/SO(N-1)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-07T15:14:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuum limit",
      "spin chains",
      "non-compact bosons",
      "euclidean black hole cft",
      "single majorana fermion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160101559V",
      "inspire": 1414220
    }
  }
}