The non-abelian Born-Infeld action at order F-6

To gain insight into the non-abelian Born-Infeld (NBI) action, we study coi nciding D-branes wrapped on tori, slid turn on magnetic fields on their wor ldvolume. We then compare predictions for the spectrum of open strings stre tching between these D-branes, from perturbative string theory and from the effective NBI action. Under some plausible assumptions, we find correction s to the Str-prescription for the NBI action at order FS. In the process we give a way to classify terms in the NBI action that can he written in term s of field strengths only, in terms of permutation group theory. (C) 2001 E lsevier Science B.V. All rights reserved.