Hypermultiplets, domain walls and supersymmetric attractors

We establish general properties of supersymmetric flow equations and of the superpotential of five-dimensional N=2 gauged supergravity coupled to vector multiplets and hypermultiplets. We provide necessary and sufficient conditions for BPS domain walls and find a set of algebraic attractor equations for N=2 critical points. As an example we describe in detail the gauging of the universal hypermultiplet and a vector multiplet. We study a two-parameter family of superpotentials with supersymmetric AdS critical points and we find, in particular, an N=2 embedding for the UV-IR solution of Freedman, Gubser, Pilch, and Warner of the N=8 theory. We comment on the relevance of these results for brane world constructions.