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

Counting the Massive Vacua of N=1* Super Yang-Mills Theory