Perturbatively Exact $w_{1+\infty}$ Asymptotic Symmetry of Quantum Self-Dual Gravity

TL;DR

This paper demonstrates that the $w_{1+ ablafty}$ asymptotic symmetry algebra in quantum self-dual gravity remains unchanged at the quantum level, despite known loop corrections, indicating its perturbative exactness.

Contribution

It shows that the classical $w_{1+ ablafty}$ algebra persists without quantum corrections in quantum self-dual gravity, extending the classical symmetry to the quantum regime.

Findings

The $w_{1+ ablafty}$ algebra is preserved at one-loop in quantum self-dual gravity.

Quantum corrections do not alter the asymptotic symmetry algebra in this setting.

The algebra's persistence suggests its perturbative exactness in the quantum theory.

Abstract

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 $w_{1+\infty}$ 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 $w_{1+\infty}$ algebra persists in quantum self-dual gravity without corrections.