  To gain insight into the non-abelian Born-Infeld (NBI) action, we study
coinciding D-branes wrapped on tori, and turn on magnetic fields on their
worldvolume. We then compare predictions for the spectrum of open strings
stretching between these D-branes, from perturbative string theory and from the
effective NBI action. Under some plausible assumptions, we find corrections to
the Str-prescription for the NBI action at order F^6. In the process we give a
way to classify terms in the NBI action that can be written in terms of field
strengths only, in terms of permutation group theory.
