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A bstract The infinite tower of positive-helicity soft gravitons in any minimally coupled, tree-level, asymptotically flat four-dimensional (4D) gravity was recently shown to generate a  w  1+∞  asymptotic symmetry algebra. It is natural to ask whether this classical algebra acquires quantum corrections at loop level. We explore this in quantum self-dual gravity, whose amplitudes acquire known one-loop exact all-plus helicity quantum corrections. We show using collinear splitting formulae that, remarkably, the  w  1+∞  algebra persists in quantum self-dual gravity without corrections.

Perturbatively exact w1+∞ asymptotic symmetry of quantum self-dual gravity