Counting the massive vacua of N=1*super Yang-Mills theory

We compute the number of massive vacua of N = 4 supersymmetric Yang-Mills theory on R-4 mass-deformed to preserve N = 1 supersymmetry, for any gauge group G. We use semi-classical techniques and efficiently reproduce the known counting for A, B and C type gauge groups, present the generating function for both O(2n) and SO(2n), and compute the supersymmetric index for gauge groups of exceptional type. A crucial role is played by the classification of nilpotent orbits, as well as global properties of their centralizers. We give illustrative examples of new features of our analysis for the D-type algebras.