BPS States of the Non-Abelian Born-Infeld Action

TL;DR

This work demonstrates that the trace structure of the non-abelian Born–Infeld action can be fixed by requiring BPS-like worldvolume configurations to linearise the action and minimise energy. By analyzing instantons in D4-branes, monopoles/dyons in D3-branes, vortices in D2-branes, and Nahm data from D-strings, the author shows that Tseytlin’s symmetrised trace ($STr$) uniquely yields a determinant that can be written as a sum of squares under BPS conditions, reducing the action to Yang–Mills theory on these configurations. The results connect a network of dual brane realizations and support the view that only the $STr$ structure preserves the necessary BPS properties for the non-abelian BI action. These findings also point toward a natural supersymmetric extension and provide a clearer understanding of multi-brane dynamics within the NBI framework.

Abstract

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. The T-dual worldvolume theories of D-strings and D0-branes are also considered. 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. The worldvolume energy of such configurations is an absolute minimum. It would seem, moreover, that such an analysis holds for the symmetrised trace structure of Tseytlin's proposal only.