  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.

High Energy Physics - Theory