  We (numerically) construct new static, asymptotically AdS solutions where the
conformal infinity is the product of time and S^2 x S^1. There always exist a
family of solutions in which the S^1 is not contractible and, for small S^1,
there are two additional families of solutions in which the S^1 smoothly
pinches off. This shows that (when fermions are antiperiodic around the S^1)
there is a quantum phase transition in the gauge theory as one decreases the
radius of the S^1 relative to the S^2. We also compare the masses of our
solutions and argue that the one with lowest mass should minimize the energy
among all solutions with conformal boundary S^2 x S^1 x R. This provides a new
positive energy conjecture for asymptotically locally AdS metrics. A simple
analytic continuation produces AdS black holes with topology S^2 x S^1.
