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We consider the twistor description of conformal higher spin theories andgive twistor space actions for the self-dual sector of theories with spingreater than two that produce the correct flat space-time spectrum. We identifya ghost-free subsector, analogous to the embedding of Einstein gravity withcosmological constant in Weyl gravity, which generates the unique spin-sthree-point anti-MHV amplitude consistent with Poincare invariance and helicityconstraints. By including interactions between the infinite tower ofhigher-spin fields we give a geometric interpretation to the twistor equationsof motion as the integrability condition for a holomorphic structure on aninfinite jet bundle. Finally, we introduce anti-self-dual interaction terms todefine a twistor action for the full conformal higher spin theory.

Conformal Higher Spin Theory and Twistor Space Actions