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A class of conformally flat and asymptotically anti-de Sitter geometriesinvolving profiles of scalar fields is studied from the point of view of gaugedsupergravity. The scalars involved in the solutions parameterise theSL(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. Thesegeometries descend via consistent truncation from distributions of D3-branes,M2-branes, or M5-branes in ten or eleven dimensions. We exhibit analogoussolutions asymptotic to AdS_6 which descend from the D4-D8-brane system. Weobtain the related six-dimensional theory by consistent reduction from massivetype IIA supergravity. All our geometries correspond to states in the Coulombbranch of the dual conformal field theories. We analyze linear fluctuations ofminimally coupled scalars and find both discrete and continuous spectra, butalways bounded below.Comment: Latex, 38 pages, minor correction

Symmetric potentials of gauged supergravities in diverse dimensions and Coulomb branch of gauge theories