{
  "id": "2006.05070",
  "version": "v1",
  "published": "2020-06-09T06:34:25.000Z",
  "updated": "2020-06-09T06:34:25.000Z",
  "title": "Conformal invariance from scale invariance in non-linear sigma models",
  "authors": [
    "Yu Nakayama"
  ],
  "comment": "14 pages",
  "categories": [
    "hep-th"
  ],
  "abstract": "There exists a certain argument that in even dimensions, scale invariant quantum field theories are conformal invariant. We may try to extend the argument in $2n + \\epsilon$ dimensions, but the naive extension has a small loophole, which indeed shows an obstruction in non-linear sigma models in $2+\\epsilon$ dimensions. Even though it could have failed due to the loophole, we show that scale invariance does imply conformal invariance of non-linear sigma models in $2+\\epsilon$ dimension from the seminal work by Perelman on the Ricci flow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-09T06:34:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-linear sigma models",
      "scale invariance",
      "conformal invariance",
      "scale invariant quantum field theories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}