Comments on supersymmetric solutions of minimal gauged supergravity in five dimensions

We investigate supersymmetric solutions of minimal gauged supergravity in five dimensions, in the timelike class. We propose an ansatz based on a four-dimensional local orthotoric Kähler metric and reduce the problem to a single sixth-order equation for two functions, each of one variable. We find an analytic, asymptotically locally AdS solution comprising five parameters. For a conformally flat boundary, this reduces to a previously known solution with three parameters, representing the most general solution of this type known in the minimal theory. We discuss the possible relevance of certain topological solitons contained in the latter to account for the supersymmetric Casimir energy of dual superconformal field theories on ${S}^{3}\times {\mathbb{R}}$. Although we obtain a negative response, our analysis clarifies several aspects of these solutions. In particular, we show that there exists a unique regular topological soliton in this family.