Celestial $w_{1+\infty}$ symmetries from twistor space
Abstract
We explain how twistor theory represents the selfdual 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 selfdual 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 treelevel perturbative gravity recently discovered in the context of celestial amplitudes. We use a twistor sigma model for the selfdual sector which describes maps from the Riemann sphere to the asymptotic twistor space defined from characteristic data at null infinity. 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. We also discuss how the two copies of $Lw_{1+\infty}$, one for each of the selfdual and antiselfdual sectors, are represented in the OPEs of vertex operators of the 4d ambitwistor string.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.06066
 Bibcode:
 2021arXiv211006066A
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 27 pages, 1 figure. v2: Added action of soft algebra on negative helicity gravitons in Sec. 4.3, references added