• DOI:10.3842/SIGMA.2022.016
• Corpus ID: 238634139

Celestial w1+∞ Symmetries from Twistor Space

@article{Adamo2022CelestialWS,
  title={Celestial w1+∞ Symmetries from Twistor Space},
  author={Tim Adamo and Lionel Mason and Atul Sharma},
  journal={Symmetry, Integrability and Geometry: Methods and Applications},
  year={2022}
}

• T. Adamo, L. Mason, Atul Sharma
• Published 12 October 2021
• Mathematics
• Symmetry, Integrability and Geometry: Methods and Applications

. 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 nonlinear graviton construction. The symmetries of the self-dual sector are generated by the corresponding loop algebra Lw 1+ ∞ of the algebra w 1+ ∞ 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 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+ ∞ . The vertex operators representing soft gravitons in our model act as currents generating the wedge algebra of w 1+ ∞ and produce the expected celestial OPE with hard gravitons of both helicities. We also discuss how the two copies of Lw 1+ ∞ , 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.