Stability in Einstein-Scalar Gravity with a Logarithmic Branch
arXiv:1112.3964 · doi:10.1103/PhysRevD.85.106011
Abstract
We investigate the non-perturbative stability of asymptotically anti-de Sitter gravity coupled to tachyonic scalar fields with mass saturating the Breitenlohner-Freedman bound. Such "designer gravity" theories admit a large class of boundary conditions at asymptotic infinity. At this mass, the asymptotic behavior of the scalar field develops a logarithmic branch, and previous attempts at proving a minimum energy theorem failed due to a large radius divergence in the spinor charge. In this paper, we finally resolve this issue and derive a lower bound on the conserved energy. Just as for masses slightly above the BF bound, a given scalar potential can admit two possible branches of the corresponding superpotential, one analytic and one non-analytic. The key point again is that existence of the non-analytic branch is necessary for the energy bound to hold. We discuss several AdS/CFT applications of this result, including the use of double-trace deformations to induce spontaneous symmetry breaking.
31 pages, 7 figures
References in corpus (11)
- Building an AdS/CFT superconductor
- Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields
- Towards a Novel no-hair Theorem for Black Holes
- New stability results for Einstein scalar gravity
- Multitrace deformations, Gamow states, and Stability of AdS/CFT
- Supersymmetric Multi-trace Boundary Conditions in AdS
- Holographic quantum criticality from multi-trace deformations
- Josephson Junctions and AdS/CFT Networks
- Update on Cosmic Censorship Violation in AdS
- Remarks on Resonant Scalars in the AdS/CFT Correspondence
- Spherical perturbations of hairy black holes in designer gravity theories