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 zero 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.