  We study theories with sixteen supercharges and a discrete energy spectrum.
One class of theories has symmetry group $SU(2|4)$. They arise as truncations
of ${\cal N}=4$ super Yang Mills. They include the plane wave matrix model, 2+1
super Yang Mills on $R \times S^2$ and ${\cal N}=4$ super Yang Mills on $R
\times S^3/Z_k$. We explain how to obtain their gravity duals in a unified way.
We explore the regions of the geometry that are relevant for the study of some
1/2 BPS and near BPS states. This leads to a class of two dimensional (4,4)
supersymmetric sigma models with non-zero $H$ flux, including a massive
deformed WZW model. We show how to match some features of the string spectrum
with the Yang Mills theory.
  The other class of theories are also connected to ${\cal N}=4$ super Yang
Mills and arise by making some of the transverse scalars compact. Their vacua
are characterized by a 2d Yang Mills theory or 3d Chern Simons theory. These
theories realize peculiar superpoincare symmetry algebras in 2+1 or 1+1
dimensions with "non-central" charges. We finally discuss gravity duals of
${\cal N}=4$ super Yang Mills on $AdS_3 \times S^1$.
