{
  "id": "2011.06328",
  "version": "v1",
  "published": "2020-11-12T11:51:59.000Z",
  "updated": "2020-11-12T11:51:59.000Z",
  "title": "A Derivation of AdS/CFT for Vector Models",
  "authors": [
    "Ofer Aharony",
    "Shai M. Chester",
    "Erez Y. Urbach"
  ],
  "comment": "71 pages + appendices (2 figures)",
  "categories": [
    "hep-th"
  ],
  "abstract": "We explicitly rewrite the path integral for the free or critical $O(N)$ (or $U(N)$) bosonic vector models in $d$ space-time dimensions as a path integral over fields (including massless high-spin fields) living on ($d+1$)-dimensional anti-de Sitter space. Inspired by de Mello Koch, Jevicki, Suzuki and Yoon and earlier work, we first rewrite the vector models in terms of bi-local fields, then expand these fields in eigenmodes of the conformal group, and finally map these eigenmodes to those of fields on anti-de Sitter space. Our results provide an explicit (non-local) action for a high-spin theory on anti-de Sitter space, which is presumably equivalent in the large $N$ limit to Vasiliev's classical high-spin gravity theory (with some specific gauge-fixing to a fixed background), but which can be used also for loop computations. Our mapping is explicit within the $1/N$ expansion, but in principle can be extended also to finite $N$ theories, where extra constraints on products of bulk fields need to be taken into account.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-12T11:51:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "derivation",
      "vasilievs classical high-spin gravity theory",
      "dimensional anti-de sitter space",
      "path integral",
      "bosonic vector models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 71,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}