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

Adam Ball; Sruthi Narayanan; Jakob Salzer; Andrew Strominger

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arXiv · 2111.10392

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

Adam Ball·Sruthi Narayanan·Jakob Salzer·Andrew Strominger

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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.

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Adam Ball, Sruthi Narayanan, Jakob Salzer, Andrew Strominger. 2021-11-19. Perturbatively Exact $w_{1+\infty}$ Asymptotic Symmetry of Quantum Self-Dual Gravity. https://arxiv.org/abs/2111.10392

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