New stability results for Einstein scalar gravity

TL;DR

This paper investigates stability conditions for Einstein-scalar gravity in anti-de Sitter space, extending known energy bounds to broader boundary conditions, with implications for dual field theories in gauge/gravity duality.

Contribution

It extends stability results for asymptotically AdS gravity with scalar fields, allowing for more general boundary conditions characterized by an arbitrary function W.

Findings

Energy remains bounded even when W is arbitrarily negative.

Stable ground states can exist with certain negative boundary conditions.

Implications for adding negative double trace operators in dual field theories.

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 $V(\phi)$ 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.