BPS states of the non-abelian Born–Infeld action

We argue that the trace structure of the non-abelian Born–Infeld action can be fixed by demanding that the action be linearised by certain energy-minimising BPS-like configurations. It is shown how instantons in D4-branes, SU(2) monopoles and dyons in D3-branes, and vortices in D2-branes are all BPS states of the action recently proposed by Tseytlin. All such configurations can be dealt with exactly within the context of non-abelian Born–Infeld theory since, given the relevant BPS-like condition, the action reduces to that of Yang–Mills theory. It would seem, moreover, that such an analysis holds for the symmetrised trace structure of Tseytlinʹs proposal only.