Bound states in N = 4 SYM on T^3: Spin(2n) and the exceptional groups

Understand

The low energy spectrum of (3+1)-dimensional N=4 supersymmetric Yang-Mills theory on a spatial three-torus contains a certain number of bound states, characterized by their discrete abelian magnetic and electric 't Hooft fluxes.

• At weak coupling, the wave-functions of these states are supported near points in the moduli space of flat connections where the unbroken gauge group is semi-simple.
• The number of such states is related to the number of normalizable bound states at threshold in the supersymmetric matrix quantum mechanics with 16 supercharges based on this unbroken group.
• Mathematically, the determination of the spectrum relies on the classification of almost commuting triples with semi-simple centralizers.