Trees, Self Dual Gravity, Gravity MHV Amplitudes, Lw1+infinity

Based on https://arxiv.org/abs/2408.11139 . In this talk we'll explain how self-dual metrics (which correspond to spacetimes containing only positive helicity gravitons) can be written as a sum over connected "tree" diagrams, which are different from Feynman diagrams. If we add two anti-self-dual perturbations to the spacetime and evaluate the on-shell action of said spacetime, we can give a first principles proof of the NSVW tree formula for graviton MHV scattering in Einstein gravity. Time permitting we'll also discuss how the tree formula in SDG can be used to express the action of the so-called Lw1+infinity algebra on metrics in self dual gravity.