On Topologically Massive Gravity with Extended Supersymmetry

We describe the construction of $2+1$-dimensional toplogically massive adS gravity with $\mathcal{N}$-extended supersymmetry in superspace by means of introducing a compensating hypermultiplet for the super-Weyl invariance. For $\mathcal{N}\ge 3$ the scalar multiplet must be on shell and the potential for the scalar compensator is completely determined by the geometry. As a consequence the resulting massive theory has no free parameter for $\mathcal{N}\ge 4$. For $\mathcal{N}=4$ we show that this leads to topologically massive gravity at the chiral point and construct the corresponding off-shell component action.