Gauge and matter fields coupled to N = 2 supergravity

Abstract

We consider the potential of a general matter system of N = 2 vector and scalar multiplets coupled to supergravity. For lagrangians that are initially quadratic in the matter fields we prove that the potential is either positive or unbounded from below. Our results have been obtained in the framework of a superconformal multiplet calculus, and we have verified that they can be derived from each of the three off-shell representations. As an example we consider SO(6) Yang-Mills theory coupled to scalar multiplets in the 10 + representation, which, for suitably chosen parameters, leads to the potential of gauged N = 8 supergravity. We discuss possibilities for residual nonabelian symmetry groups after breaking of N = 8 super-symmetry to N = 1 or 2.