Superconformal matter coupling in three dimensions and topologically massive gravity

The coupling of supersymmetric scalar-matter multiplets to superconformal gauge theory and gravity in three-dimensional space-time is described in the formalism of N-extended superspace. The formulations of super-gauge theory and conformal supergravity in this superspace are reviewed and a formalism for analysing superfield components is developed. A superfield action principle giving rise to a general class of minimal on-shell multiplets is introduced. Subsequently, a scalar multiplet described by a constrained superfield and consisting only of Lorentz scalars and spinors transforming under spin(N) is recognised as a specially constrained case of the minimal unconstrained multiplet. Its superfield action is deduced from the action principle for the unconstrained scalar superfield. The analysis is generalised to a super-gauge- and supergravity-covariant description of superfield components and a coupling condition for the scalar multiplet as well as the action describing this coupling are obtained. Based on this, all gauge groups for the scalar multiplet consistent with N $\le$ 8 extended superconformal symmetry are determined in at superspace, as well as in curved superspace where the scalar multiplet is also coupled to conformal supergravity. This results in the construction of all superconformal Chern-Simons-matter theories coupled to gravity. Using the gravitationally coupled scalar multiplet as a conformal compensator, the resulting cosmological topologically massive supergravities are classified with regard to the corresponding parameters $\mu \ell$, i.e. the product of the conformal-gravity coupling and the anti-de Sitter radius. The modifications of $\mu \ell$ in presence of possible gauge couplings for the scalar compensator are determined.