From 0-branes to torons

Abstract The moduli space of 0-branes on T 4 gives a prediction for the moduli space of torons in U ( n ) super-Yang-Mills theory which preserve 16 supersymmetries. The 0-brane number corresponds to the greatest common denominator of the rank n , magnetic fluxes and the instanton number. This prediction is derived using U -duality. We explicitly check this prediction by analyzing U ( n ) bundles with non-zero first as well as second Chern classes. The argument is extended to deduce the moduli space of torons which preserve 8 supersymmetries. Parts of the discussion extend naturally to T 2 and T 3 . Some of the U -dualities involved are related to Lorentz boosts along the eleventh direction in M-theory.