The gauge invariance of the non-Abelian Chern-Simons action for D-branes revisited

TL;DR

This paper proves the gauge invariance of the non-Abelian D-brane action under various gauge transformations, clarifying the role of background gauge transformations and T-duality, without requiring massive dielectric couplings.

Contribution

It introduces a precise method to demonstrate gauge invariance of the non-Abelian D-brane action, including massive gauge transformations, and confirms consistency with T-duality.

Findings

The non-Abelian D-brane action is invariant under R-R and NS-NS gauge transformations.

Massive gauge invariance does not require massive dielectric couplings.

Results are consistent with (massive) T-duality for N D9-branes.

Abstract

We present an elegant method to prove the invariance of the Chern-Simons part of the non-Abelian action for N coinciding D-branes under the R-R and NS-NS gauge transformations, by carefully defining what is meant by a background gauge transformation in the non-Abelian world volume action. We study as well the invariance under massive gauge transformations of the massive Type IIA supergravity and show that no massive dielectric couplings are necessary to achieve this invariance. We show that this result is consistent with (massive) T-duality from the non-Abelian action for N D9-branes.