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 functionW. An important open question is to determine whichW 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 (φ) admits a suitable superpotential. We extend this result and show that the energy remains bounded even in some cases whereW 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.