Conformal supergravity in three dimensions: off-shell action

Using the off-shell formulation for N-extended conformal supergravity in three dimensions that has recently been presented in arXiv:1305.3132, we construct superspace actions for conformal supergravity theories with N < 6. For each of the cases considered, we work out the complete component action as well as the gauge transformation laws of the fields belonging to the Weyl supermultiplet. The N = 1 and N = 2 component actions derived coincide with those proposed by van Nieuwenhuizen and Rocek in the mid-1980s. The off-shell N = 3, N = 4 and N = 5 supergravity actions are new results. Upon elimination of the auxiliary fields, these actions reduce to those constructed by Lindstrom and Rocek in 1989 (and also by Gates and Nishino in 1993).