w(1+infinity) and the Celestial Sphere

TL;DR

Strominger demonstrates that the infinite array of plus-helicity soft graviton symmetries in tree-level, asymptotically flat 4D gravity can be organized into a chiral 2D Kac-Moody algebra derived from the wedge algebra of $w_{1+\infty}$, with soft photon and gluon symmetries transforming irreducibly under the same structure. By mapping tree-level soft currents to celestial CFT currents and employing an $SL(2,\mathbb{R})_{\rm w}$ covariant light-ray transform, the authors show that the complete soft symmetry algebra collapses to the wedge subalgebra of $w_{1+\infty}$, featuring only positive weights. They extend the construction to gauge theory, obtaining a $GL(\infty,\mathbb{R})$ Kac-Moody structure with consistent cross-relations to gravity currents, reinforcing a unified celestial symmetry framework. The work further speculates on quantization leading to a quantum $W_{1+\infty}$ deformation and discusses broader connections to celestial holography, self-dual gravity, and string-theoretic contexts.

Abstract

It is shown that the infinite tower of tree-level soft graviton symmetries in asymptotically flat 4D quantum gravity can be organized into a single chiral 2D Kac-Moody symmetry based on the wedge algebra of w(1+infinity). The infinite towers of soft photon or gluon symmetries also transform irreducibly under w(1+infinity).