BPS States of the Non-Abelian Born-Infeld Action

TL;DR

This paper demonstrates that the non-abelian Born-Infeld action's trace structure can be determined by its BPS configurations, which reduce the action to Yang-Mills theory and minimize energy, confirming the validity of Tseytlin's symmetrised trace proposal.

Contribution

It shows how BPS states fix the trace structure of the non-abelian Born-Infeld action, supporting Tseytlin's symmetrised trace formulation.

Findings

BPS configurations reduce the action to Yang-Mills theory.

Energy of BPS states is an absolute minimum.

Analysis supports Tseytlin's symmetrised trace proposal.

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.