The Weak Coupling Spectrum around Isolated Vacua in N=4 Super Yang-Mills on T³ with any Gauge Group

The moduli space of flat connections for maximally supersymmetric Yang-Mills theories, in a space-time of the form T^3xR, contains isolated points, corresponding to normalizable zero energy states, for certain simple gauge groups G. We consider the low energy effective field theories in the weak coupling limit supported on such isolated points and find that when quantized they consist of an infinite set of harmonic oscillators whose angular frequencies are completely determined by the Lie algebra of G. We then proceed to find the isolated flat connections for all simple G and subsequently specify the corresponding effective field theories.