Complete superspace classification of three-dimensional Chern-Simons-matter theories coupled to supergravity

For extended N <= 8 supersymmetry we classify all possible gauge groups for a scalar multiplet allowed by the algebras of global and local supersymmetry in three dimensions. A detailed discussion of supersymmetry enhancement is included. For the corresponding topologically massive gravity with negative cosmological constant the mass of the graviton is determined algebraically as a function of N and the possible gauge couplings