The Superconformal Gaugings in Three Dimensions

Abstract : We show how three-dimensional superconformal theories for any number N<9 of supersymmetries can be obtained by taking a conformal limit of the corresponding three-dimensional gauged supergravity models. The superconformal theories are characterized by an embedding tensor that satisfies a linear and quadratic constraint. We analyze these constraints and give the general solutions for all cases. We find new N=4,5 superconformal theories based on the exceptional Lie superalgebras F(4), G(3) and D(2|1;a). Using the supergravity connection we discuss which massive deformations to expect. As an example we work out the details for the case of N=6 supersymmetry.