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We construct an action for the superconformal Chern-Simons theory withnon-Abelian gauge groups in three-dimensional N=3 projective superspace. Wepropose a Lagrangian given by the product of the function of the tropicalmultiplet, that represents the N=3 vector multiplet, and the O(-1,1) multiplet.We show how the tropical multiplet is embedded into the O(-1,1) multiplet bycomparing our Lagrangian with the Chern- Simons Lagrangian in the N=2superspace. We also discuss N=4 generalization of the action.

Non-Abelian Chern-Simons Actions in Three-dimensional Projective Superspaces