Higher order terms in the non-abelian D-brane effective action and magnetic background fields

TL;DR

This paper verifies the non-abelian D-brane effective action up to fourth order in alpha' by comparing the spectrum in magnetic backgrounds with string theory, confirming the proposed expressions and discussing future applications.

Contribution

It provides a detailed check of the non-abelian D-brane effective action at fourth order in alpha' using magnetic background spectra, confirming the theoretical proposal.

Findings

Perfect agreement with string theory results

Correction of a typo in the original expression

Validation of the proposed effective action at fourth order

Abstract

Recently a proposal for the non-abelian effective D-brane action was given through fourth order in alpha'. As the resulting expressions turned out to be quite involved, some checks of this result are called for. In the present paper we calculate the spectrum in the presence of constant magnetic background fields and compare it to the string theoretical result. Apart from a small typo in the original expression (the overall sign of thefourth order term), we obtain perfect agreement. We discuss potential applications.