{
  "id": "2209.09250",
  "version": "v1",
  "published": "2022-09-19T18:00:00.000Z",
  "updated": "2022-09-19T18:00:00.000Z",
  "title": "An embedding formalism for CFTs in general states on curved backgrounds",
  "authors": [
    "Enrico Parisini",
    "Kostas Skenderis",
    "Benjamin Withers"
  ],
  "comment": "6 pages, 1 figure",
  "categories": [
    "hep-th",
    "gr-qc",
    "math.DG"
  ],
  "abstract": "We present a generalisation of the embedding space formalism to conformal field theories (CFTs) on non-trivial states and curved backgrounds, based on the ambient metric of Fefferman and Graham. The ambient metric is a Lorentzian Ricci-flat metric in $d+2$ dimensions and replaces the Minkowski metric of the embedding space. It is canonically associated with a $d$-dimensional conformal manifold, which is the physical spacetime where the CFT${}_d$ lives. We propose a construction of CFT${}_d$ correlators in non-trivial states and on curved backgrounds using appropriate geometric invariants of the ambient space as building blocks. As a test of the formalism we apply it to thermal 2-point functions and find exact agreement with a holographic computation and expectations based on thermal operator product expansions (OPEs).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-19T18:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "curved backgrounds",
      "general states",
      "embedding formalism",
      "thermal operator product expansions",
      "ambient metric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}