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.
Conformal Higher Spin Theory and Twistor Space Actions
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abstract
We consider the twistor description of conformal higher spin theories and give twistor space actions for the self-dual sector of theories with spin greater than two that produce the correct flat space-time spectrum. We identify a ghost-free subsector, analogous to the embedding of Einstein gravity with cosmological constant in Weyl gravity, which generates the unique spin-s three-point anti-MHV amplitude consistent with Poincare invariance and helicity constraints. By including interactions between the infinite tower of higher-spin fields we give a geometric interpretation to the twistor equations of motion as the integrability condition for a holomorphic structure on an infinite jet bundle. Finally, we introduce anti-self-dual interaction terms to define a twistor action for the full conformal higher spin theory.
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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.