SUPERSYMMETRIC INDEX OF THREE-DIMENSIONAL GAUGE THEORY

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| ≥ 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.