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We study off-shell N-extended Yang-Mills multiplets coupled to conformalsupergravity in three spacetime dimensions. Superform formulations arepresented for the non-Abelian Chern-Simons actions in the cases N=1, 2, 3, andthe corresponding component actions are explicitly worked out. Such aChern-Simons action does not exist for N=4. In the latter case, a superformformulation is given for the BF term that describes the coupling of two Abelianvector multiplets with self-dual and anti-self-dual superfield strengthsrespectively. The superform results obtained are used to construct linearmultiplet action principles in the cases N=2, 3, 4. The N=3 and N=4 actions aredemonstrated to be universal in the sense that all known off-shellsupergravity-matter systems (with the exception of pure conformal supergravity)may be described using such an action. Starting from the N=3 and N=4 Abelianvector multiplets, we also construct composite O(2) multiplets which areanalogues of the four-dimensional construction of an N=2 reduced chiral scalarengineered from the improved tensor multiplet. Using these composites, wepresent the superfield equations of motion for N=3 and N=4 anti-de Sitter andtopologically massive supergravity theories. We also sketch the construction ofa large family of higher derivative couplings for N=3 and N=4 vectormultiplets.

Supergravity-matter actions in three dimensions and Chern-Simons terms