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We construct off-shell superconformal actions of hypermultiplets coupled withnon-Abelian gauge multiplets in three-dimensional N = 3 and N = 4 projectivesuperspaces. We establish the explicit embeddings of the N = 2 vector andadjoint chiral superfields, that constitute the N = 4 gauge multiplets, intothe tropical multiplets. We also construct the action in the four-dimensional N= 2 projective superspace.

Non-Abelian Gauge Groups and Hypermultiplets in Projective Superspaces