Abstract:We prove a `nonlinear graviton theorem' for higher-spin self-dual gravity. We consider small deformations of the complex structure of the non-projective twistor space that are bounded in a specified region near the origin and investigate the space $M_{HS}$ of holomorphically embedded complex planes $\mathbb{C}^2$ that intersect the origin. We show that this space is an infinite dimensional complex manifold with a canonical projection onto a four-dimensional holomorphic self-dual spacetime $\mathcal{M}$, and discuss the geometry induced on this new higher-spin space. Solutions of higher-spin self-dual gravity are then obtained by choosing an embedding of spacetime $\mathcal{M}$ into higher-spin space $M_{HS}$, with higher-spin symmetries arising from the different choices of embedding. Integrability of the theory is manifested in the form of a Lax pair for the system that we present. We conjecture that chiral higher-spin gravity can similarly be realized by considering deformations that are unconstrained at the origin.
From: Yannick Herfray [view email]
[v1]
Wed, 17 Jun 2026 15:15:53 UTC (57 KB)
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