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arXiv · 1006.2387

New stability results for Einstein scalar gravity

Thomas Faulkner·Gary T. Horowitz·Matthew M. Roberts
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Abstract

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 $V(ϕ)$ 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.

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Thomas Faulkner, Gary T. Horowitz, Matthew M. Roberts. 2010-06-11. New stability results for Einstein scalar gravity. https://doi.org/10.1088/0264-9381%2F27%2F20%2F205007

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