Higher-spin self-dual gravity arises by embedding 4D spacetime into an infinite-dimensional manifold of holomorphic planes in a boundedly deformed twistor space, with higher-spin symmetries from different embeddings and integrability via a Lax pair.
Notes on Higher-Spin Diffeomorphisms,
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Higher-spin self-dual gravity from holomorphic planes in twistor space
Higher-spin self-dual gravity arises by embedding 4D spacetime into an infinite-dimensional manifold of holomorphic planes in a boundedly deformed twistor space, with higher-spin symmetries from different embeddings and integrability via a Lax pair.