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

TL;DR

This paper constructs exact self-dual pp-wave solutions in chiral higher-spin gravity with zero cosmological constant, revealing solutions that satisfy both linear and non-linear equations of motion and are sourced by a positive-helicity spin-2 field.

Contribution

It introduces a novel class of exact solutions in chiral higher-spin gravity using a light-cone and Kerr-Schild ansatz, extending understanding of self-dual backgrounds.

Findings

Solutions satisfy both linear and non-linear equations of motion.

Solutions are sourced by a positive-helicity spin-2 field.

Higher-order vertices are annihilated, indicating free-field behavior on the background.

Abstract

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.