World-Volume Interactions on D-Branes

TL;DR

This paper investigates how massless open-string fields on D$p$-branes interact with background closed-string fields by computing a range of string scattering amplitudes. By comparing these amplitudes to expanded Born-Infeld and Chern-Simons actions, the authors show that leading low-energy world-volume interactions are captured by these actions only if the background fields are functional of the non-Abelian transverse scalars $X^i$ and the pull-backs are defined with covariant derivatives $D_aX^i$. They derive explicit linear and quadratic couplings, demonstrating consistency with the non-Abelian BI/CS framework and highlighting the role of the background’s functional dependence on the scalars. The work further discusses ambiguities in non-Abelian ordering and the need for higher-point amplitudes to fully resolve them, with physical implications such as dipole couplings and bound-state interpretations (e.g., D2–D0 systems) emerging from specific non-Abelian configurations.

Abstract

We examine in detail various string scattering amplitudes in order to extract the world-volume interactions of massless fields on a Dirichlet brane. We find that the leading low-energy interactions are consistent with the Born-Infeld and Chern-Simons actions. In particular, our results confirm that the background closed string fields appearing in these actions must be treated as functionals of the non-abelian scalar fields describing transverse fluctuations of the D-brane.