  A class of conformally flat and asymptotically anti-de Sitter geometries
involving profiles of scalar fields is studied from the point of view of gauged
supergravity. The scalars involved in the solutions parameterise the
SL(N,R)/SO(N) submanifold of the full scalar coset of the gauged supergravity,
and are described by a symmetric potential with a universal form. These
geometries descend via consistent truncation from distributions of D3-branes,
M2-branes, or M5-branes in ten or eleven dimensions. We exhibit analogous
solutions asymptotic to AdS_6 which descend from the D4-D8-brane system. We
obtain the related six-dimensional theory by consistent reduction from massive
type IIA supergravity. All our geometries correspond to states in the Coulomb
branch of the dual conformal field theories. We analyze linear fluctuations of
minimally coupled scalars and find both discrete and continuous spectra, but
always bounded below.
