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

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