Self-dual pp-wave solutions in chiral higher-spin gravity

We show that chiral higher-spin gravity with a vanishing cosmological constant admits a class of exact self-dual pp-wave solutions derived from harmonic scalar functions and two principal spinors. These solutions satisfy both the linear and non-linear equations of motion, as they annihilate all higher-order vertices, leading to the equations of motion for free fields on a self-dual background sourced by a positive-helicity spin-2 field. Our method employs a simple light-cone ansatz for positive-helicity chiral higher-spin fields, along with a modified Kerr-Schild ansatz adapted for the self-dual gravity framework.