Symmetric potentials of gauged supergravities in diverse dimensions and Coulomb branch of gauge theories - art. no. 086003

A class of conformally flat and asymptotically anti-de Sitter geometries in volving profiles of scalar fields is studied from the point of view of gaug ed supergravity. The scalars involved in the solutions parametrize 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 geo metries descend via consistent truncation from distributions of D3-branes, M2-branes, or M5-branes in ten or eleven dimensions. We exhibit analogous s olutions asymptotic to AdS(6) which descend from the D4-D8-brane system. We obtain the related six-dimensional theory by consistent reduction from mas sive type IIA supergravity. All our geometries correspond to states in the Coulomb branch of the dual conformal field theories. We analyze linear fluc tuations of minimally coupled scalars and find both discrete and continuous spectra, but always bounded below.