${\mathrm{w}}_{1+\infty }$ Algebra and the Celestial Sphere: Infinite Towers of Soft Graviton, Photon, and Gluon Symmetries

It is shown that the infinite tower of tree-level plus-helicity 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 ${\mathrm{w}}_{1+\infty }$, which naturally acts on the celestial sphere at null infinity. The infinite towers of soft photon or gluon symmetries also transform irreducibly under ${\mathrm{w}}_{1+\infty }$.