  We construct an action for the superconformal Chern-Simons theory with
non-Abelian gauge groups in three-dimensional N=3 projective superspace. We
propose a Lagrangian given by the product of the function of the tropical
multiplet, 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 by
comparing our Lagrangian with the Chern- Simons Lagrangian in the N=2
superspace. We also discuss N=4 generalization of the action.

High Energy Physics - Theory