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We (numerically) construct new static, asymptotically AdS solutions where theconformal infinity is the product of time and S^2 x S^1. There always exist afamily 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 smoothlypinches 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 theradius of the S^1 relative to the S^2. We also compare the masses of oursolutions and argue that the one with lowest mass should minimize the energyamong all solutions with conformal boundary S^2 x S^1 x R. This provides a newpositive energy conjecture for asymptotically locally AdS metrics. A simpleanalytic continuation produces AdS black holes with topology S^2 x S^1.Comment: 17 pages, 4 figures, v2: minor changes, added reference

Gravity dual of gauge theory onS2×S1×R

Gravity dual of gauge theory onS²×S¹×R