AdS-CFT correspondence and a new positive energy conjecture for general relativity - art. no. 026005

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 agr eement with the expected negative Casimir energy in the field theory. The s tability of the gauge theory would imply that this supergravity solution ha s minimum energy among all solutions with the same boundary conditions. Hen ce we are led to conjecture a new positive energy theorem for asymptoticall y locally anti-de Sitter spacetimes. We show that the candidate minimum ene rgy solution is stable against all quadratic fluctuations of the metric. [S 0556-2821(98)07824-2].