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We present the inverse Penrose transform (the map from spacetime to twistorspace) for self-dual Yang-Mills (SDYM) and its higher-spin extensions on a flatbackground. The twistor action for the higher-spin extension of SDYM (HS-SDYM)is of BF-type. By considering a deformation away from the self-dual sector ofHS-SDYM, we discover a new action that describes a higher-spin extension ofYang-Mills theory (HS-YM). The twistor action for HS-YM is a straightforwardgeneralization of the Yang-Mills one.

Twistor Constructions for Higher-spin Extensions of (Self-dual) Yang-Mills