We establish general properties of supersymmetric flow equations and of the superpotential of five-dimensional $\mathcal{N}=2\mathrm{}$ 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 $\mathcal{N}=2\mathrm{}$ 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 $\mathcal{N}=2\mathrm{}$ embedding for the UV-IR solution of Freedman, Gubser, Pilch, and Warner of the $\mathcal{N}=8\mathrm{}$ theory. We comment on the relevance of these results for brane world constructions.

• Received 27 April 2001

DOI:https://doi.org/10.1103/PhysRevD.64.104006