Minimal N= 4 topologically massive supergravity

Using the superconformal framework, we construct a new off-shell model for N= 4 topologically massive supergravity which is minimal in the sense that it makes use of a single compensating vector multiplet and involves no free parameter. As such, it provides a counterexample to the common lore that two compensating multiplets are required within the conformal approach to supergravity with eight supercharges in diverse dimensions. This theory is an off-shell N= 4 supersymmetric extension of chiral gravity. All of its solutions correspond to non-conformally flat superspaces. Its maximally supersymmetric solutions include the so-called critical (4,0) anti-de Sitter superspace introduced in [25], and well as warped critical (4,0) anti-de Sitter superspaces. We also propose a dual formulation for the theory in which the vector multiplet is replaced with an off-shell hypermultiplet. Upon elimination of the auxiliary fields belonging to the hypermultiplet and imposing certain gauge conditions, the dual action reduces to the one introduced in [20].