New stability results for Einstein scalar gravity

We consider asymptotically anti de Sitter gravity coupled to a scalar field with mass slightly above the Breitenlohner-Freedman bound. This theory admits a large class of consistent boundary conditions characterized by an arbitrary function W. An important open question is to determine which W admit stable ground states. It has previously been shown that the total energy is bounded from below if W is bounded from below, and the bulk scalar potential V(phi) admits a suitable superpotential. We extend this result and show that the energy remains bounded even in some cases where W can become arbitrarily negative. As one application, this leads to the possibility that in gauge/gravity duality, one can add a double trace operator with negative coefficient to the dual field theory and still have a stable vacuum.