All Order Self-Dual Correlators From Symmetries

Abstract

We consider the scalar actions for self-dual Yang-Mills and self-dual gravity. We give a novel resummed version of their infinite tower of symmetries. We show that the Ward identities for symmetries corresponding to the individual levels of the infinite tower give the soft limits for wavefunction coefficients, while their resummed version completely fixes the full wavefunction. Our analysis is valid for general boundary conditions. Finally, we give an explicit formula for the $n$-point wavefunction coefficient as a single determinant reorganising the perturbiner solution, which also satisfies the soft limits.