Getting the D-brane effective action from BPS configurations

TL;DR

This paper derives the non-abelian D-brane effective action from BPS configurations, confirming the Born-Infeld form and matching string theory spectra, thus resolving ordering ambiguities in the action.

Contribution

It introduces a method to determine the non-abelian open superstring effective action from BPS solutions, including derivative terms, up to order ^3.

Findings

Derived the full effective action through ^3 order.

Confirmed the Born-Infeld structure as the unique deformation.

Achieved perfect agreement with string theory spectra.

Abstract

We review a method to find the non-abelian open superstring effective action, thereby settling the issue of the ordering ambiguities. We start from solutions to Yang-Mills which, in D-brane context, define certain BPS configurations. Studying their deformations in the abelian case shows that the Born-Infeld action is the unique deformation which admits solutions of this type. By applying the method to the non-abelian case we calculated the full effective action through O(\alpha'^3). The presence of derivative terms turns out to be essential. Testing the result by comparing the spectrum in the presence of a constant magnetic background field with the string theory prediction, we obtain perfect agreement.