Anti-deSitter Vacua of Gauged Supergravities with 8 Supercharges

Abstract

We investigate supersymmetric extrema of Abelian gauged supergravity theories with non-trivial vector multiplets and 8 supercharges in four and five dimensions. The scalar fields of these models parameterize a manifold consisting of disconnected branches and restricting to the case where this manifold has a non-singular metric we show that on every branch there can be at most one extremum, which is a local maximum (for W>0) or a minimum (for W<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).

Figures (2)

• Figure 1: The scalar fields of vector super-multiplets of D=5 theory parameterize a manifold that consists of different branches and due to the attractor equations point where the normal vector is parallel to a given constant vector $\alpha_I$ are "fixed-points" or extrema of the superpotential. The straight lines correspond to F=0 domain and shaded areas to $F < 0$ domains.
• Figure 2: Restricting to a region where the kinetic part of the scalar fields is strictly positive definite, any critical point, where $\partial_A W(\phi^A) =0$, is either a minimum (for $W>0$) or a maximum (for $W<0$). Since saddle points are also excluded, the critical points cannot be connected in a regular way.