Gravity Dual of Gauge Theory on S² x S¹ x R

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.