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A covariant twistor action for chiral higher-spin theory in anti--de Sitter and flat space is constructed in term of a holomorphic Chern-Simons theory on twistor space. The action reproduces all known cubic vertices of chiral higher-spin theory in flat space. The spacetime action of the holomorphic Chern-Simons theory in flat space is also obtained.
Tung Tran (Tue,) studied this question.
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