  We consider the subset of gauged maximal supergravities that consists of the
SO(n+1) gauge fields A^{ij} and the scalar deformation T^{ij} of the S^n in the
spherical reduction of M-theory or type IIB. We focus on the Abelian Cartan
subgroup and the diagonal entries of T^{ij}. The resulting theories can be
viewed as the STU models with additional hyperscalars. We find that the
theories with only one or two such vectors can be generalized naturally to
arbitrary dimensions. The same is true for the D=4 or 5 Einstein-Maxwell theory
with such a hyperscalar. The gauge fields become massive, determined by
stationary points of the hyperscalars a la the analogous Abelian Higgs
mechanism. We obtain classes of Lifshitz and Schrodinger vacua in these
theories. The scaling exponent z turns out to be rather restricted, taking
fractional or irrational numbers. Tweaking the theories by relaxing the mass
parameter or making a small change of the superpotential, we find that
solutions with z=2 can emerge. In a different application, we find that the
resolution of superstar singularity in the STU models by using bubbling-AdS
solitons can be generalized to arbitrary dimensions in our theories. In
particular, we obtain the smooth AdS solitons that can be viewed as the
resolution of the Reissner-Nordstrom superstars in general dimensions.
