AdS-CFT correspondence and a new positive energy conjecture for general relativity

We examine the AdS-CFT correspondence when gauge theory is considered on a compactified space with supersymmetry-breaking boundary conditions. We find that the corresponding supergravity solution has a negative energy, in agreement with the expected negative Casimir energy in the field theory. The stability of the gauge theory would imply that this supergravity solution has minimum energy among all solutions with the same boundary conditions. Hence we are led to conjecture a new positive energy theorem for asymptotically locally anti--de Sitter spacetimes. We show that the candidate minimum energy solution is stable against all quadratic fluctuations of the metric.