On the gauge invariance and coordinate transformations of non-Abelian D-brane actions

TL;DR

This paper investigates the gauge invariance and coordinate transformation properties of non-Abelian D-brane actions, revealing how worldvolume fields and embedding scalars transform under NS-NS gauge transformations and T-duality.

Contribution

It demonstrates the non-trivial transformation of embedding scalars under NS-NS gauge transformations and proves the invariance of the non-Abelian Chern-Simons action, providing insights into non-Abelian coordinate transformations.

Findings

Embedding scalars transform as al X q [X, X] under NS-NS gauge transformations

Non-Abelian Chern-Simons action is invariant under these transformations

T-duality relates NS-NS gauge transformations to coordinate transformations

Abstract

We study the variations of the worldvolume fields in the non-Abelian action for multiple D-branes. Using T-duality we find that the embedding scalars transform non-trivially under NS-NS gauge transformations as \delta X ~ [X, X] and prove that the non-Abelian Chern-Simons action is invariant under these transformations. Given that T-duality relates the (part of the) NS-NS transformation with (part of the) general coordinate transformations, we can get some insight in the structure of non-Abelian coordinate transformations.