Higher-Derivative Corrections to the Non-Abelian Born-Infeld Action

TL;DR

This paper computes higher-derivative corrections to the non-abelian Born-Infeld action in open superstring theory up to order alpha'^4, revealing non-symmetrised trace terms crucial for D-brane physics beyond slow variation approximations.

Contribution

It provides explicit higher-derivative terms in the non-abelian Born-Infeld action up to order alpha'^4, including non-symmetrised trace corrections, derived from string scattering amplitudes.

Findings

Higher-derivative terms involve non-symmetrised traces.

Corrections are significant for studying D-branes beyond slow variation.

Order alpha'^4 corrections impact fluctuation spectrum calculations.

Abstract

We determine higher-derivative terms in the open superstring effective action with U(N) gauge group up to and including order alpha'^4 as can be extracted from 4 boson, 2 boson - 2 fermion and 4 fermion string scattering amplitudes. This yields corrections to the non-abelian Born-Infeld action involving higher derivatives as is relevant for studying D-branes beyond the slowly varying field approximation. While at order alpha'^2 the action has recently been shown to be a symmetrised trace, this no longer is true at order alpha'^3 or alpha'^4. We argue that these terms including higher derivatives are as important in a low-energy expansion as e.g. the much-discussed alpha'^4 F^6 terms. In particular a computation of the fluctuation spectra at order alpha'^4 has to take into account these non-symmetrised trace higher-derivative terms computed here.