{
  "id": "2209.02421",
  "version": "v1",
  "published": "2022-09-06T11:37:48.000Z",
  "updated": "2022-09-06T11:37:48.000Z",
  "title": "Reconstruction of a vertex algebra in higher dimensions from its one-dimensional restriction",
  "authors": [
    "Bojko Bakalov",
    "Nikolay M. Nikolov"
  ],
  "comment": "19 pages",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "math.QA"
  ],
  "abstract": "Vertex algebras in higher dimensions correspond to models of quantum field theory with global conformal invariance. Any vertex algebra in higher dimensions admits a restriction to a vertex algebra in any lower dimension, and in particular, to dimension one. In this paper, we find natural conditions under which the converse passage is possible. These conditions include a unitary action of the conformal Lie algebra with a positive energy, which is given by local endomorphisms and obeys certain integrability properties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-06T11:37:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vertex algebra",
      "one-dimensional restriction",
      "reconstruction",
      "conformal lie algebra",
      "higher dimensions admits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}