Fivebranes from gauge theory

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 $AdS_3 \times S^1$.