Counting the massive vacua of Nn =n n 1n ∗n n n n super Yang-Mills theory

摘要

We compute the number of massive vacua of ( mathcal{N}=4 ) supersymmetric Yang-Mills theory on ( {mathrm{mathbb{R}}}^4 ) mass-deformed to preserve ( mathcal{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