Bound states in Script N = 4 SYM onT3: Spin(2n) and the exceptional groups

Abstract

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 elecric '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 super symmetric matrix quantum mechanics wit h 1 6 supercharges based on this unbroken group. Mathematic ally, the determination of the spectrum relies on the classification of almost commuting triples with semi-simple centralizers. We complete the work begun in a previous paper, by computing the spectrum of bound states in theories based on the even-dimensional spin groups and the exceptional groups. The results satisfy the constraints of S-duality in a rather non-trivial way.