  We construct a class of theories with 16 supersymmetries on spheres of
dimension nine and less. The gauge coupling and mass terms for the scalar
fields depend on the polar angle away from the north pole. Assuming finite
coupling on the north pole, this leads to zero coupling at the south pole for
$d>4$ and infinite coupling at the south pole for $d<4$. The underlying
supersymmetry algebra of these theories is shown to be isomorphic to the
Poincar\'e superalgebra in $d$-dimensions. We also give a localization
procedure which leads to nontrivial results for $d=2$.
