Celestial w _1+∞ Symmetries from Twistor Space

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 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 treelevel 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.

Topics & Concepts