{
  "id": "2208.11179",
  "version": "v1",
  "published": "2022-08-23T20:14:33.000Z",
  "updated": "2022-08-23T20:14:33.000Z",
  "title": "Celestial chiral algebras, colour-kinematics duality and integrability",
  "authors": [
    "Ricardo Monteiro"
  ],
  "comment": "21 pages, 1 figure",
  "categories": [
    "hep-th"
  ],
  "abstract": "We study celestial chiral algebras appearing in celestial holography, using the light-cone gauge formulation of self-dual Yang-Mills theory and self-dual gravity, and explore also a deformation of the latter. The recently discussed $w_{1+\\infty}$ algebra in self-dual gravity arises from the soft expansion of an area-preserving diffeomorphism algebra, which plays the role of the kinematic algebra in the colour-kinematics duality and the double copy relation between the self-dual theories. The $W_{1+\\infty}$ deformation of $w_{1+\\infty}$ arises from a Moyal deformation of self-dual gravity. This theory is interpreted as a constrained chiral higher-spin gravity, where the field is a tower of higher-spin components fully constrained by the graviton component. In all these theories, the chiral structure of the operator-product expansion exhibits the colour-kinematics duality: the implicit `left algebra' is the self-dual kinematic algebra, while the `right algebra' provides the structure constants of the operator-product expansion, ensuring its associativity. In a scattering amplitudes version of the Ward conjecture, the left algebra ensures the classical integrability of this type of theories. In particular, it enforces the vanishing of the tree-level amplitudes via the double copy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-23T20:14:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "colour-kinematics duality",
      "integrability",
      "operator-product expansion",
      "kinematic algebra",
      "study celestial chiral algebras appearing"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}