The non-abelian Born-Infeld action at order F^6

TL;DR

This paper investigates the non-abelian Born-Infeld action at order F^6 by comparing string theory spectra with effective action predictions, revealing corrections to existing prescriptions and classifying terms using permutation group theory.

Contribution

It introduces a method to classify NBI action terms at order F^6 using permutation group theory and identifies corrections to the Str-prescription.

Findings

Corrections to the Str-prescription at order F^6.

A classification scheme for NBI terms based on permutation groups.

Consistency between string spectra and effective action predictions.

Abstract

To gain insight into the non-abelian Born-Infeld (NBI) action, we study coinciding D-branes wrapped on tori, and turn on magnetic fields on their worldvolume. We then compare predictions for the spectrum of open strings stretching between these D-branes, from perturbative string theory and from the effective NBI action. Under some plausible assumptions, we find corrections to the Str-prescription for the NBI action at order F^6. In the process we give a way to classify terms in the NBI action that can be written in terms of field strengths only, in terms of permutation group theory.