On the Stability of Warped Anti-de Sitter Spaces in Supergravity

Abstract

We discuss the perturbative stability of warped anti-de Sitter (WAdS${}_3$) spaces in three-dimensional gauged supergravity. To this end, we first derive the analogue of the Breitenlohner-Freedman bound for a single scalar field on such a curved background. We then apply this analysis to the half-maximal $D=3$ gauged supergravity obtained from the compactification of the $D=6$, $\mathcal{N}=(1,1)$ supergravity on S${}^3$. Families of three-dimensional configurations, uplifting to spaces of the form ${\mathrm{WAdS}}_3\times {\mathrm{WS}}^3$, are found by turning on appropriate vector and scalar fields, supporting the AdS${}_3$ and S${}^3$ warpings, respectively. Finally, we show that the spectra of scalar fluctuations satisfy the stability criteria for each solution.

28 pages, including appendices