{
  "id": "2110.06066",
  "version": "v3",
  "published": "2021-10-12T15:15:04.000Z",
  "updated": "2022-03-08T06:42:38.000Z",
  "title": "Celestial $w_{1+\\infty}$ Symmetries from Twistor Space",
  "authors": [
    "Tim Adamo",
    "Lionel Mason",
    "Atul Sharma"
  ],
  "comment": "Dedicated to our friend and mentor Roger Penrose on the occasion of his 90th birthday and the recent award of his Nobel prize in physics",
  "journal": "SIGMA 18 (2022), 016, 23 pages",
  "doi": "10.3842/SIGMA.2022.016",
  "categories": [
    "hep-th",
    "gr-qc"
  ],
  "abstract": "We explain how twistor theory represents the self-dual sector of four dimensional gravity in terms of the loop group of Poisson diffeomorphisms of the plane via Penrose's non-linear graviton construction. The symmetries of the self-dual sector are generated by the corresponding loop algebra $Lw_{1+\\infty}$ of the algebra $w_{1+\\infty}$ of these Poisson diffeomorphisms. We show that these coincide with the infinite tower of soft graviton symmetries in tree-level perturbative gravity recently discovered in the context of celestial amplitudes. We use a twistor sigma model for the self-dual sector which describes maps from the Riemann sphere to the asymptotic twistor space defined from characteristic data at null infinity ${\\mathcal I}$. We show that the OPE of the sigma model naturally encodes the Poisson structure on twistor space and gives rise to the celestial realization of $Lw_{1+\\infty}$. The vertex operators representing soft gravitons in our model act as currents generating the wedge algebra of $w_{1+\\infty}$ and produce the expected celestial OPE with hard gravitons of both helicities. We also discuss how the two copies of $Lw_{1+\\infty}$, one for each of the self-dual and anti-self-dual sectors, are represented in the OPEs of vertex operators of the 4d ambitwistor string.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2022-03-08T06:42:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "self-dual sector",
      "poisson diffeomorphisms",
      "vertex operators representing soft gravitons",
      "penroses non-linear graviton construction",
      "asymptotic twistor space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}