Anti–de Sitter vacua of gauged supergravities with 8 supercharges

Abstract

We investigate supersymmetric extrema of Abelian gauged supergravity theories with nontrivial vector multiplets and 8 supercharges in four and five dimensions. The scalar fields of these models parametrize a manifold consisting of disconnected branches and, restricting to the case where this manifold has a nonsingular metric, we show that on every branch there can be at most one extremum, which is a local maximum (for $W>\mathrm{}0)$ or a minimum (for $W<\mathrm{}0)$ of the superpotential W. Therefore, these supergravity models do not allow for regular domain wall solutions interpolating between different extrema of the superpotential and the space-time transverse to the wall asymptotically always approaches the boundary of AdS (UV-fixed points in a dual field theory).