  In N=1 super Yang-Mills theory in three spacetime dimensions, with a simple
gauge group $G$ and a Chern-Simons interaction of level $k$, the supersymmetric
index $\Tr (-1)^F$ can be computed by making a relation to a pure Chern-Simons
theory or microscopically by an explicit Born-Oppenheimer calculation on a
two-torus. The result shows that supersymmetry is unbroken if $|k|\geq h/2$
(with $h$ the dual Coxeter number of $G$) and suggests that dynamical
supersymmetry breaking occurs for $|k|<h/2$. The theories with large $|k|$ are
massive gauge theories whose universality class is not fully described by the
standard criteria.
